Question

question 8
vertical angles are complementary angles.
always true
sometimes true
never true
question 9
what is the individual measure of a pair of supplementary vertical angles?
30 degrees
45 degrees
60 degrees
90 degrees

Explanation:

Step1: Recall angle - definitions

Vertical angles are equal. Complementary angles add up to 90 degrees. Since vertical angles can have any measure, they are not always complementary. So for question 8, the answer is never true.

Step2: Use supplementary and vertical - angle properties

Let the measure of each vertical angle be \(x\). Since they are supplementary, \(x + x=180^{\circ}\). Solving the equation \(2x = 180^{\circ}\), we get \(x = 90^{\circ}\). So for question 9, the individual measure of a pair of supplementary vertical angles is 90 degrees.

Answer:

Question 8: C. Never true
Question 9: D. 90 degrees