Question

The measure of one angle is 7 times the measure of its complement. What is the measure of the larger angle?

a) 70°
b) 77°
c) 63°
d) 84°

Answer 1

The measure of the larger angle is 77°.

Step-by-step explanation:

To solve this problem, we can set up an equation using the fact that the measure of one angle is 7 times the measure of its complement. Let's call the measure of the smaller angle x. The measure of the larger angle, then, would be 7x. We know that the sum of the measures of two complementary angles is 90 degrees, so we can write the equation: x + 7x = 90. Simplifying the equation, we get 8x = 90. Dividing both sides by 8, we find x = 11.25. Therefore, the measure of the larger angle is 7 times 11.25, which is 78.75 degrees. Since we need to choose from the options provided, the closest option is 77° (option b).