Question

name: ky - math date: per: unit 1: geometry basics homework 6: angle relationships this is a 2 - page document! 1. find the missing measure. 2. find the missing measure. 3. find the missing measures. 4. if the measure of an angle is 13°, find the measure of its supplement. 5. if the measure of an angle is 38°, find the measure of its complement.

Explanation:

Step1: Recall angle - relationship rules

Complementary angles add up to 90° and supplementary angles add up to 180°. Vertical angles are equal.

Step2: Solve for question 1

The given angle is 65°. Since the two angles are complementary (the right - angle symbol indicates a 90° total), we use the formula \(x + 65=90\). Then \(x = 90 - 65\).
\[x=25\]

Step3: Solve for question 2

The two angles are vertical angles. Vertical angles are equal. So if one angle is 51°, then \(x = 51\).

Step4: Solve for question 3

The 107° angle and \(y\) are supplementary, so \(y+107 = 180\), then \(y=180 - 107=73\). The 107° angle and \(x\) are vertical angles, so \(x = 107\). The \(z\) and \(y\) are vertical angles, so \(z = 73\).

Step5: Solve for question 4

If an angle is 13°, and its supplement is \(s\), then \(13 + s=180\), so \(s = 180 - 13=167\).

Step6: Solve for question 5

If an angle is 38°, and its complement is \(c\), then \(38 + c=90\), so \(c = 90 - 38 = 52\).

Answer:

1. \(x = 25\)
2. \(x = 51\)
3. \(x = 107\), \(y = 73\), \(z = 73\)
4. The measure of the supplement is 167°
5. The measure of the complement is 52°