Question

problem 1

1. how do you know that the two indicated angles are supplementary? what is their sum?
2. find the measure of ∠x. show your steps.
3. what do you notice about the measure of ∠x and ∠y? what is this angle pair called?
4. find the measure of ∠y.

Explanation:

Step1: Recall supplementary - angle definition

Supplementary angles sum to 180°.

Step2: Answer question 1

The two angles are supplementary because they form a linear - pair (adjacent angles on a straight line). Their sum is 180°.

Step3: Find measure of ∠x

Since the 45° angle and ∠x are supplementary, we use the formula ∠x+45° = 180°. Then ∠x=180° - 45° = 135°.

Step4: Analyze ∠x and ∠y

∠x and ∠y are congruent (equal in measure). They are called corresponding angles (assuming the lines are parallel).

Step5: Find measure of ∠y

Since ∠x and ∠y are corresponding angles and ∠x = 135°, then ∠y=135°.

Answer:

1. They form a linear - pair, sum is 180°.
2. ∠x = 135°
3. They are equal, called corresponding angles.
4. ∠y = 135°