Question

evaluate independent practice lesson 10.2 homework complete problems a2, 3, 5, 7, 9, and 17 for independent practice. when you are finished, check the solutions with your teacher. find m∠1 and m∠2. tell which theorem you use in each case. (see example 1.) 3) 5)

Explanation:

Problem 3

Step1: Find $m\angle1$ (supplementary angles)

$\angle1$ and $117^\circ$ are supplementary, so:
$$m\angle1 = 180^\circ - 117^\circ = 63^\circ$$
Theorem: Same-Side Interior Angles Theorem (since the lines are parallel, same-side interior angles are supplementary).

Step2: Find $m\angle2$ (corresponding angles)

$\angle2$ and the $117^\circ$ angle are corresponding angles, so:
$$m\angle2 = 117^\circ$$
Theorem: Corresponding Angles Theorem (parallel lines cut by transversal, corresponding angles are congruent).

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Problem 5

Step1: Find $m\angle2$ (supplementary angles)

$\angle2$ and $122^\circ$ are supplementary, so:
$$m\angle2 = 180^\circ - 122^\circ = 58^\circ$$
Theorem: Same-Side Interior Angles Theorem (parallel lines cut by transversal, same-side interior angles are supplementary).

Step2: Find $m\angle1$ (corresponding angles)

$\angle1$ and the $122^\circ$ angle are corresponding angles, so:
$$m\angle1 = 122^\circ$$
Theorem: Corresponding Angles Theorem (parallel lines cut by transversal, corresponding angles are congruent).

Answer:

Problem 3:

$m\angle1 = 63^\circ$ (Same-Side Interior Angles Theorem)
$m\angle2 = 117^\circ$ (Corresponding Angles Theorem)

Problem 5:

$m\angle1 = 122^\circ$ (Corresponding Angles Theorem)
$m\angle2 = 58^\circ$ (Same-Side Interior Angles Theorem)