Exercise 24 Page 593

First, we will illustrate the given information in a diagram. If we let x be the measure of the smaller acute angle, then the measure of the larger acute angle is 8x.

According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. 8x+x= 90 Let's solve this equation.

The measure of the smaller acute angle is x=10. Now, we can find the measure of the greater acute angle. 8x ⇒ 8(10) = 80