Geometry Parallel Lines and Angles Quiz

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Questions and Answers

What is the value of x when 4x - 15 = 105?

  • 25
  • 35
  • 30 (correct)
  • 20

Which theorem justifies the equation (2x + 5)° = 75° when determining line parallelism?

  • Converse Corresponding Angles Postulate (correct)
  • Alternate Interior Angles Theorem
  • Linear Pair Theorem
  • Transversal Postulate

If the angle on line r is 85°, what is the measure of the angle on line s if they are considered alternate exterior angles?

  • 85° (correct)
  • 62°
  • 107°
  • 108°

What is the correct next step after solving 2x + 5 = 75?

<p>x = 35 (B)</p> Signup and view all the answers

According to the Alternate Exterior Angles theorem, what is concluded if (2x - 23)° = 85°?

<p>The lines are parallel. (C)</p> Signup and view all the answers

What is the first step to isolate x in the equation 2x + 5 = 75?

<p>Subtract 5 from both sides. (B)</p> Signup and view all the answers

If it is known that lines r and s are parallel, what can be inferred about corresponding angles on these lines?

<p>Corresponding angles are equal. (D)</p> Signup and view all the answers

Which postulate supports the conclusion for finding angle measures when two lines are cut by a transversal?

<p>Converse Corresponding Angles Postulate (D)</p> Signup and view all the answers

What is the value of x when solving the equation $2x - 23 = 85$?

<p>54 (B)</p> Signup and view all the answers

Calculate the value of x from the equation $5x - 15 = 3x + 17$.

<p>16 (C)</p> Signup and view all the answers

What is the relationship between the angles $5x - 10$ and $3x + 44$ when they form a linear pair?

<p>They add up to 180°. (D)</p> Signup and view all the answers

What is the final value of x when solving the equation $8x + 34 = 180$?

<p>18.25 (D)</p> Signup and view all the answers

Given two parallel lines l and m, what is the angle measure of angle a if it is given as 64°?

<p>64° (A)</p> Signup and view all the answers

Using the Linear Pair Theorem, if angle b measures 116°, what is the measure of the adjacent angle?

<p>180° - 116° (C)</p> Signup and view all the answers

What type of theorem is used to determine that angle c measures 116° given that it is an alternate exterior angle?

<p>Alternate Exterior Angles Theorem (C)</p> Signup and view all the answers

If $l$ // $m$ and $n$ // $o$, what can be inferred about angle relationships formed by these parallel lines?

<p>Alternate interior angles are equal. (A)</p> Signup and view all the answers

Which theorem justifies the parallel lines given ∠1 = ∠2 with transversal line u?

<p>Converse Corr. Angles Postulate (C)</p> Signup and view all the answers

What conclusion can be drawn from the relation ∠5 = ∠7 using transversal line v?

<p>Lines <em>r</em> and <em>s</em> are parallel by Converse Alt.Int. Theorem (B)</p> Signup and view all the answers

When ∠3 = ∠2 is given, what is the status of the lines with respect to parallelism?

<p>Cannot be determined with no transversal (D)</p> Signup and view all the answers

Based on the equation m∠3 + m∠6 = 180, what can be concluded about lines u and v?

<p>They are parallel by the Converse Consecutive Interior Angles Theorem (C)</p> Signup and view all the answers

Given that ∠3 ≈ ∠6, what can be said about the two lines with transversal line s?

<p>The lines cannot be concluded as parallel because angles are not equal (A)</p> Signup and view all the answers

Which theorem can be used to validate the parallelism of lines given that m∠6 is 122° and referenced by ∠4?

<p>Alternate Interior Angles Theorem (D)</p> Signup and view all the answers

If ∠5 is given as 110°, what can be inferred about the relationship with angle ∠1?

<p>They are parallel through the Corresponding Angles Postulate (C)</p> Signup and view all the answers

Why can't the parallelism of the lines be determined when ∠3 and ∠6 are given as 122°?

<p>The angles do not correspond with a transversal (A)</p> Signup and view all the answers

Flashcards

Finding x for parallel lines (1)

If two angles are supplementary and one of them is equal to (4x-15) degrees and the other is 105 degrees, we can find the value of x by setting the angles to be equal in measure, finding that x equals 30.

Finding x for parallel lines (2)

If two angles are in corresponding position in relation to two parallel lines and an intersecting line, then we can set them equal and solve for x to find that x = 35.

Parallel lines and alternate exterior angles

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Parallel lines and linear pairs

If two lines are parallel, then linear pairs formed by the transversal are supplementary.

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Variable calculation (3)

With two parallel lines (r and s), and alternate exterior angles are given, you can find the value of the variable x by setting the given angle measure equal to the alternate exterior angle, finding that 2x-23 = 85, and subsequently solve for x to find a solution.

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Consecutive interior angles

Two angles are supplementary if they are consecutive interior angles when two parallel lines are cut by a transversal.

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Supplementary angles

Two angles are supplementary if their sum equals 180 degrees.

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Corresponding Angles postulate

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

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Solving Equation 2x - 23 = 85

Isolate 'x' by adding 23 to both sides, then dividing both sides by 2 to find the value of x.

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Finding angle x when 5x-15 = 3x +17

To solve for x, collect terms with x on one side of the equation

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Finding angle x with (5x - 10)°, (3x + 44)° and consecutive ext. Ls

Use the property that consecutive exterior angles of parallel lines add up to 180 degrees. Then solve for x.

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Vertical angles

Vertical angles are opposite angles formed by intersecting lines.

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Linear Pair Theorem

Adjacent angles that form a straight line on a plane add up to 180° .

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Alternate Exterior Angles

Angles that lie outside a pair of lines and on opposite sides of the transversal.

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Solving Linear Equation in Flashcards

Isolating a unknown variable (x) to solve algebraic equations.

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Parallel Lines and Transversals

Parallel lines are lines in a plane that do not intersect; a transversal is a line that intersects two or more coplanar lines.

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Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

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Vertical Angles Theorem

Vertical angles are congruent.

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Converse Corresponding Angles Postulate

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

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Converse Alternate Interior Angles Theorem

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

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Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

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Parallel Lines Converse

If a transversal forms congruent or supplementary angles with two lines, then the two lines are parallel.

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Related Documents

Unit 3B Angle Pairs Review PDF

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