We know that the measure of one of the acute angles in a right triangle is 5 times the measure of the other acute angle in the triangle. Let's illustrate this information with a diagram.
We want to find the measure of each acute angle. To do so, we will let x be the measure of the smaller acute angle. Then, the measure of the larger acute angle is 5x. According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. This means that the sum of the measures of each acute angle has to be equal to 90.
5x+x=90
We will use the equation to find the value of x. Let's do it!
The measure of the smaller acute angle is 15^(∘). Now we can find the measure of the greater acute angle by substituting this value into the expression 5x.
