Question

Angles 9 and 10 are corresponding and complementary angles formed by two parallel lines cut by a transversal. Find the measure of angle 9 (Hint: complementary angles add up to 90 degrees).

a) What is the measure of angle 9?

45 degrees
60 degrees
75 degrees
90 degrees

Answer 1

Angles 9 and 10 are corresponding and complementary angles formed by two parallel lines cut by a transversal. The measure of angle 9 can be found by subtracting the measure of angle 10 from 90 degrees.

Step-by-step explanation:

Corresponding angles are pairs of angles that are in the same position relative to the parallel lines. Complementary angles are pairs of angles that add up to 90 degrees. Since angles 9 and 10 are corresponding and complementary angles, we know that the sum of their measures is 90 degrees. Therefore, the measure of angle 9 is 90 minus the measure of angle 10.

Let's say that the measure of angle 10 is x degrees. Since angle 9 and angle 10 are complementary, we can write the equation:

9° + x° = 90°

Solving for x, we get:

x = 90° - 9°

x = 81°

So, the measure of angle 9 is 81 degrees.