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Questions and Answers
LMNOP is a regular pentagon. Determine the measure of (\angle OLN).
LMNOP is a regular pentagon. Determine the measure of (\angle OLN).
36°
LMNOP is a regular pentagon. What kind of triangle is (\triangle LON)? Explain how you know.
LMNOP is a regular pentagon. What kind of triangle is (\triangle LON)? Explain how you know.
Isosceles triangle. The two sides of the triangle (LO and LN) are congruent because it is a regular pentagon.
Sandy designed this logo for the jerseys worn by her softball team. She told the graphic artist that each interior angle of the regular decagon should measure $162^\circ$, based on this calculation: (S(10) = \frac{180^\circ(10-1)}{10})( S(10) = \frac{1620^\circ}{10}) (S(10) = 162^\circ) Identify the error she made and determine the correct angle.
Sandy designed this logo for the jerseys worn by her softball team. She told the graphic artist that each interior angle of the regular decagon should measure $162^\circ$, based on this calculation: (S(10) = \frac{180^\circ(10-1)}{10})( S(10) = \frac{1620^\circ}{10}) (S(10) = 162^\circ) Identify the error she made and determine the correct angle.
The numerator of the formula for S(10) should be 180°(10 – 2); S(10) = 144°.
Martin is planning to build a hexagonal picnic table, as shown. Determine the angles at the ends of each piece of wood that Martin needs to cut for the seats.
Martin is planning to build a hexagonal picnic table, as shown. Determine the angles at the ends of each piece of wood that Martin needs to cut for the seats.
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Martin is planning to build a hexagonal picnic table, as shown. How would these angles change if Martin decided to make an octagonal table instead?
Martin is planning to build a hexagonal picnic table, as shown. How would these angles change if Martin decided to make an octagonal table instead?
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Three exterior angles of a convex pentagon measure 70°, 60°, and 90°. The other two exterior angles are congruent. Determine the measures of the interior angles of the pentagon.
Three exterior angles of a convex pentagon measure 70°, 60°, and 90°. The other two exterior angles are congruent. Determine the measures of the interior angles of the pentagon.
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Determine the sum of the measures of the indicated angles.
Determine the sum of the measures of the indicated angles.
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In each figure, the congruent sides form a regular polygon. Determine the values of a, b, c, and d.
In each figure, the congruent sides form a regular polygon. Determine the values of a, b, c, and d.
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A pentagon tile has two 90° angles. The other three angles are equal. Is it possible to create a tiling pattern using only this tile? Justify your answer.
A pentagon tile has two 90° angles. The other three angles are equal. Is it possible to create a tiling pattern using only this tile? Justify your answer.
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Each interior angle of a regular polygon is five times as large as its corresponding exterior angle. What is the common name of this polygon?
Each interior angle of a regular polygon is five times as large as its corresponding exterior angle. What is the common name of this polygon?
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Determine the values of a, b, and c.
Determine the values of a, b, and c.
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Determine the value of x in the following diagrams. a) b)
Determine the value of x in the following diagrams. a) b)
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Joyce is an artist who uses stained glass to create sun catchers, which are hung in windows. Joyce designed this sun catcher using triangles and regular hexagons. Determine the measure of the interior angles of each different polygon in her design.
Joyce is an artist who uses stained glass to create sun catchers, which are hung in windows. Joyce designed this sun catcher using triangles and regular hexagons. Determine the measure of the interior angles of each different polygon in her design.
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Determine the sum of the indicated angles.
Determine the sum of the indicated angles.
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Name the pairs of corresponding angles.
Name the pairs of corresponding angles.
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Are any of the pairs you indentified in part a) equal? Explain.
Are any of the pairs you indentified in part a) equal? Explain.
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How many pairs of supplementary angles can you see in the diagram? Name one pair.
How many pairs of supplementary angles can you see in the diagram? Name one pair.
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Are there any other pairs of equal angles? If so, name them.
Are there any other pairs of equal angles? If so, name them.
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Is AB parallel to CD? Explain how you know.
Is AB parallel to CD? Explain how you know.
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Given: QR || ST Prove: ST=TR
Given: QR || ST Prove: ST=TR
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Determine the sum of the measures of the interior angles of a 15-sided regular polygon.
Determine the sum of the measures of the interior angles of a 15-sided regular polygon.
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Show that each exterior angle measures 24°.
Show that each exterior angle measures 24°.
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Given: ABCDE is a regular Pentagon. Prove: AC || ED
Given: ABCDE is a regular Pentagon. Prove: AC || ED
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Study Notes
Geometry Problems
-
Regular Pentagon (Problem 10):
- A pentagon LMNOP has interior angles equal.
- Angle ZOLN measures 36 degrees
- Triangle ALON is an isosceles triangle.
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Regular Decagon (Problem 11):
- Sandy's calculation for interior angle of a regular decagon (10 sides) was incorrect.
- The formula should use (10-2) instead of (10-1).
- The correct interior angle is 144 degrees.
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Hexagonal Picnic Table (Problem 13):
- The angles at the ends of each piece of wood for a hexagonal table are 60 degrees and 120 degrees.
- If the table was octagonal, the angles would be 67.5 degrees and 112.5 degrees.
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Convex Pentagon (Problem 14):
- Exterior angles of a convex pentagon are 70°, 60°, 90°, and two congruent unknown angles.
- The sum of the exterior angles is 360 degrees.
- Calculation shows that the other two exterior angles are equal to 75 degrees each.
- Their corresponding interior angle is 105 degrees.
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Indicated Angles Sum (Problem 15):
- The sum of indicated angles is 360 degrees.
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Regular Polygon Sides (Problem 16):
- Congruent sides forming regular polygons
- Parts (a) and (b) provide values for angles a, b, c, and d.
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Indicated Angles Sum (Problem 17):
- The sum of indicated angles is 720 degrees.
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Tiling Pattern (Problem 20):
- A pentagon tile with two 90 degree angles and three equal angles.
- A tiling pattern can be created
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Interior and Exterior Angle Relationship (Problem 21):
- An interior angle of a polygon is five times its exterior angle
- The polygon has 12 sides, a regular dodecagon.
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Self Test 1 (Problem 1):
- Values of variables a, b, and c related to angles of a polygon.
- Answer (a) :a = 70, b = 75, c = 75; (b) a = 20, b = 80, c = 100
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Value of x (Problem 2):
- Parts (a) and (b) provide values for x. -Answer (a) : x= 19; (b) x = 26
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Polygons in Suncatcher (Problem 4):
- Regular hexagons have interior angles of 120 degrees.
- Small triangles have interior angles of 60 degrees.
- Large triangles have one 120-degree angle and two 30-degree angles.
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Sum of Indicated Angles (Problem 6):
- Indicated angles sums up to 720 degrees
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Corresponding Angles (Problem 2, Problem 3):
- Pairs of corresponding angles related to parallel lines
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Parallel Lines (Problem 4):
- Proving AB is parallel to CD with the provided angles.
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Values of a, b, and c (Problem 5):
- Calculate variables a,b, and c based on given figures
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Interior angles of a 15-sided polygon (Problem 10):
- The sum of its interior angles is 2340 degrees
- Each exterior angle of the 15-sided polygon is 24 degrees
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Regular pentagon (Problem 11):
- A regular pentagon has interior angles equal in a given figure
- Lines AC and ED are parallel.
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Description
Test your understanding of geometry with this quiz focused on regular polygons including pentagons and decagons. You will solve problems related to interior and exterior angles, as well as properties of isosceles triangles. Perfect for students looking to enhance their geometry skills.
