Question

lesson 6 | session 2
4 in which figures is ∠1 = ∠2? select all that apply.
5 tell whether each statement about the figure is true or false.
a. ∠1 and ∠9 are corresponding angles.
b. ∠2 and ∠7 are alternate exterior angles.
c. ∠3 and ∠10 are alternate interior angles.
d. ∠4 and ∠7 are alternate interior angles.
6 what is the value of x? show your work.

Explanation:

4.

Step1: Recall angle - congruence rules

Vertical angles are congruent, corresponding angles in parallel - line setups are congruent, and alternate interior/exterior angles in parallel - line setups are congruent.

Step2: Analyze each figure

• In figure A, ∠1 and ∠2 are vertical angles, so ∠1 = ∠2.
• In figure B, ∠1 and ∠2 are not in a special - angle relationship (not vertical, corresponding, alternate interior or exterior) in the non - parallel line setup shown.
• In figure C, ∠1 and ∠2 are not in a special - angle relationship.
• In figure D, ∠1 and ∠2 are vertical angles, so ∠1 = ∠2.
• In figure E, ∠1 and ∠2 are corresponding angles with respect to parallel lines, so ∠1 = ∠2.
• In figure F, ∠1 and ∠2 are not in a special - angle relationship.

Step1: Recall angle - relationship definitions

• Corresponding angles are in the same relative position with respect to the transversal and parallel lines.
• Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal.
• Alternate interior angles are between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each statement

• a. ∠1 and ∠9 are corresponding angles. True.
• b. ∠2 and ∠7 are not alternate exterior angles. False.
• c. ∠3 and ∠10 are not alternate interior angles. False.
• d. ∠4 and ∠7 are alternate interior angles. True.

Step1: Identify the angle relationship

The 156° angle and the (3x + 36)° angle are same - side interior angles with respect to parallel lines. Same - side interior angles are supplementary, so their sum is 180°.

Step2: Set up the equation

156+(3x + 36)=180

Step3: Simplify the left - hand side of the equation

156+3x+36 = 192+3x
So, 192 + 3x=180

Step4: Solve for x

Subtract 192 from both sides: 3x=180 - 192=-12
Divide both sides by 3: x=-4

Answer:

A. Option A, D, E

5.