Question

problem 6

1. how did you move your hand to find ∠x? what is its measure?
2. these angles are called vertical angles. why do you think that is?
3. ∠y and ∠x are called same side interior angles. why do you think that is? what did you notice about their angle measures?
4. find the measure of ∠y. show your steps.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Since the angle adjacent to ∠x is 117°, and ∠x is a vertical angle to it, ∠x = 117°.

Step2: Recall same - side interior angles property

Same - side interior angles are on the same side of the transversal and inside the two parallel lines. For parallel lines cut by a transversal, same - side interior angles are supplementary.

Step3: Calculate the measure of ∠y

Since ∠x and ∠y are same - side interior angles and ∠x=117°, and ∠x + ∠y=180° (supplementary angles), then ∠y = 180°−117° = 63°.

Answer:

1. You can use the vertical - angle property to find ∠x. Its measure is 117°.
2. They are called vertical angles because they are opposite each other when two lines intersect. They have equal measures.
3. ∠y and ∠x are same - side interior angles because they are on the same side of the transversal and between the two parallel lines. Their angle measures are supplementary (add up to 180°).
4. ∠y = 63°