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Questions and Answers
What is the sum of the interior angles of a dodecagon?
What is the sum of the interior angles of a dodecagon?
What is the measure of one interior angle of a regular dodecagon?
What is the measure of one interior angle of a regular dodecagon?
What is the sum of the exterior angles of any polygon?
What is the sum of the exterior angles of any polygon?
A convex hexagon has exterior angles measuring 34°, 49°, 58°, 67°, and 75°. What is the measure of the sixth exterior angle?
A convex hexagon has exterior angles measuring 34°, 49°, 58°, 67°, and 75°. What is the measure of the sixth exterior angle?
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If an interior angle and an adjacent exterior angle of a polygon form a linear pair, what is the sum of their measures?
If an interior angle and an adjacent exterior angle of a polygon form a linear pair, what is the sum of their measures?
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How many diagonals does a quadrilateral have?
How many diagonals does a quadrilateral have?
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Why do vertices connected by a diagonal of a polygon have to be nonconsecutive?
Why do vertices connected by a diagonal of a polygon have to be nonconsecutive?
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What is the correct formula to find the sum of the interior angles of a polygon with n sides?
What is the correct formula to find the sum of the interior angles of a polygon with n sides?
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A regular polygon has an interior angle measuring 156°. How many sides does the polygon have?
A regular polygon has an interior angle measuring 156°. How many sides does the polygon have?
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If the sum of interior angles of a polygon is $1440°$, how many sides does the polygon have?
If the sum of interior angles of a polygon is $1440°$, how many sides does the polygon have?
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What is a regular polygon?
What is a regular polygon?
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What is the relationship between an interior angle and its corresponding exterior angle in any polygon?
What is the relationship between an interior angle and its corresponding exterior angle in any polygon?
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If each exterior angle of a regular polygon measures 9°, how many sides does it have?
If each exterior angle of a regular polygon measures 9°, how many sides does it have?
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What is the measure of each exterior angle of a regular pentagon?
What is the measure of each exterior angle of a regular pentagon?
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A regular polygon has interior angles of 165°. What is the measure of each of its exterior angles?
A regular polygon has interior angles of 165°. What is the measure of each of its exterior angles?
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Given parallelogram ABCD, with AB = $x + 4$ and CD = 12. What is the value of x?
Given parallelogram ABCD, with AB = $x + 4$ and CD = 12. What is the value of x?
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In the given two-column proof, what justifies the statement that $\angle CDA \cong \angle EDG$?
In the given two-column proof, what justifies the statement that $\angle CDA \cong \angle EDG$?
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In parallelogram ABCD, if m∠A is 65°, what is the measure of m∠C?
In parallelogram ABCD, if m∠A is 65°, what is the measure of m∠C?
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Given that $M$ bisects segment $QS$, what can be concluded about the relationship between segments $QM$ and $MS$?
Given that $M$ bisects segment $QS$, what can be concluded about the relationship between segments $QM$ and $MS$?
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If the measure of angle F in parallelogram FEGH is 60°, what is the measure of angle E?
If the measure of angle F in parallelogram FEGH is 60°, what is the measure of angle E?
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If the measure of angle $\angle ADC$ in parallelogram $ABCD$ is $110^\circ$, what is the measure of angle $\angle BCD$?
If the measure of angle $\angle ADC$ in parallelogram $ABCD$ is $110^\circ$, what is the measure of angle $\angle BCD$?
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In parallelogram JKLM, if m∠K = 50°, what is the measure of m∠L?
In parallelogram JKLM, if m∠K = 50°, what is the measure of m∠L?
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What property is used to establish that $\angle B \cong \angle F$ in the provided two-column proof?
What property is used to establish that $\angle B \cong \angle F$ in the provided two-column proof?
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In parallelogram JKLM, if m∠J = $2x$ and m∠L = $y + 3$, and m∠K = 50°, what are the values of x and y?
In parallelogram JKLM, if m∠J = $2x$ and m∠L = $y + 3$, and m∠K = 50°, what are the values of x and y?
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In a regular octagon ABCDEFGH, if sides AB and CD are extended to meet at point P, what is the measure of angle BPC?
In a regular octagon ABCDEFGH, if sides AB and CD are extended to meet at point P, what is the measure of angle BPC?
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If the measure of $\angle ADC$ is twice the measure of $\angle BCD$ in parallelogram $ABCD$, what is the measure of $\angle BCD$?
If the measure of $\angle ADC$ is twice the measure of $\angle BCD$ in parallelogram $ABCD$, what is the measure of $\angle BCD$?
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If a quadrilateral is a parallelogram, what is true about the consecutive angles?
If a quadrilateral is a parallelogram, what is true about the consecutive angles?
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Given parallelogram PQRS. If ∠P = $x$° and ∠Q = $y$°, what is the relation between $x$ and $y$?
Given parallelogram PQRS. If ∠P = $x$° and ∠Q = $y$°, what is the relation between $x$ and $y$?
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What is the relationship between opposite angles in a parallelogram?
What is the relationship between opposite angles in a parallelogram?
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Which theorem states that opposite angles of a parallelogram are congruent?
Which theorem states that opposite angles of a parallelogram are congruent?
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In the context of congruent triangles, what does the acronym 'CPCTC' refer to?
In the context of congruent triangles, what does the acronym 'CPCTC' refer to?
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What is the relationship between consecutive angles in a parallelogram?
What is the relationship between consecutive angles in a parallelogram?
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Which theorem states that the opposite sides of a parallelogram are congruent?
Which theorem states that the opposite sides of a parallelogram are congruent?
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What is a defining characteristic of the side lengths in a parallelogram?
What is a defining characteristic of the side lengths in a parallelogram?
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Given parallelogram $ABCD$, if $\angle ABC$ measures 100 degrees, what is the measure of $\angle CDA$?
Given parallelogram $ABCD$, if $\angle ABC$ measures 100 degrees, what is the measure of $\angle CDA$?
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If one angle of a parallelogram measures $70^\circ$, what is the measure of the angle opposite to it?
If one angle of a parallelogram measures $70^\circ$, what is the measure of the angle opposite to it?
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If one angle of a parallelogram measures $60^\circ$, what is the measure of a consecutive angle in the same parallelogram?
If one angle of a parallelogram measures $60^\circ$, what is the measure of a consecutive angle in the same parallelogram?
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In the given diagram with angles $(3x + 10)^\circ$, $(8x 16)^\circ$, and $(6x 19)^\circ$, what is the value of x if we assume the given angles are of a triangle?
In the given diagram with angles $(3x + 10)^\circ$, $(8x 16)^\circ$, and $(6x 19)^\circ$, what is the value of x if we assume the given angles are of a triangle?
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In the given diagram with angles $x^\circ$, $79^\circ$ and $113^\circ$, what is the value of x if we assume the given angles are of a triangle?
In the given diagram with angles $x^\circ$, $79^\circ$ and $113^\circ$, what is the value of x if we assume the given angles are of a triangle?
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In a parallelogram, if one angle measures $70^\circ$, what is the measure of the angle opposite to it?
In a parallelogram, if one angle measures $70^\circ$, what is the measure of the angle opposite to it?
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In a parallelogram, two adjacent angles measure $(b - 10)^\circ$ and $(b + 10)^\circ$. What is the value of $b$?
In a parallelogram, two adjacent angles measure $(b - 10)^\circ$ and $(b + 10)^\circ$. What is the value of $b$?
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If the measures of two consecutive angles in a parallelogram are $2m^\circ$ and $n^\circ$, and it's given that $m = 40$, what is the value of $n$?
If the measures of two consecutive angles in a parallelogram are $2m^\circ$ and $n^\circ$, and it's given that $m = 40$, what is the value of $n$?
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In the given parallelogram, one side is represented by the expression $k + 4$ and the opposite side is 8. What is the value of $k$?
In the given parallelogram, one side is represented by the expression $k + 4$ and the opposite side is 8. What is the value of $k$?
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If a parallelogram has an angle measuring $105^\circ$, what is the measure of its adjacent angle?
If a parallelogram has an angle measuring $105^\circ$, what is the measure of its adjacent angle?
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In a parallelogram, the measures of two angles are given by $5u - 10$ and $2u + 2$ respectively. If these angles are consecutive, what is the value of $u$?
In a parallelogram, the measures of two angles are given by $5u - 10$ and $2u + 2$ respectively. If these angles are consecutive, what is the value of $u$?
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In a parallelogram, one side has a length of $d - 21$ given, and its opposite side length is 20, what is the value of d?
In a parallelogram, one side has a length of $d - 21$ given, and its opposite side length is 20, what is the value of d?
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If one angle in a parallelogram is represented as $(g + 4)^\circ$ and its opposite angle is $105^\circ$, what is the value of $g$?
If one angle in a parallelogram is represented as $(g + 4)^\circ$ and its opposite angle is $105^\circ$, what is the value of $g$?
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Study Notes
Quadrilaterals and Other Polygons
- Various types of quadrilaterals exist, including parallelograms, trapezoids, and kites.
- Properties of these shapes can be used to solve problems.
Angles of Polygons
- The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180°.
- The sum of the exterior angles of any convex polygon is 360°.
- Each exterior angle of a regular n-gon measures 360°/n.
- Each interior angle of a regular n-gon measures (n-2) * 180°/n
Properties of Parallelograms
- Opposite sides of a parallelogram are congruent.
- Opposite angles of a parallelogram are congruent.
- Consecutive angles of a parallelogram are supplementary.
- The diagonals of a parallelogram bisect each other.
Properties of Special Parallelograms
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A rhombus has four congruent sides.
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The diagonals of a rhombus are perpendicular.
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A rectangle has four right angles.
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The diagonals of a rectangle are congruent.
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A square is a parallelogram with four congruent sides and four right angles.
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The diagonals of a square are congruent and perpendicular.
Properties of Trapezoids
- A trapezoid is a quadrilateral with exactly one pair of parallel sides.
- The parallel sides are called bases.
- In an isosceles trapezoid, the nonparallel sides (legs) are congruent, and the base angles are congruent.
- The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
- The diagonals of an isosceles trapezoid are congruent.
Properties of Kites
- A kite is a quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.
- The diagonals of a kite are perpendicular.
- Exactly one pair of opposite angles of a kite are congruent.
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Description
Test your knowledge on the properties of polygons, including the sums of interior and exterior angles, the number of diagonals, and relationships between angles. This quiz covers essential geometric concepts related to both regular and irregular polygons.
