Question

find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the
other acute angle.
the smaller acute angles measures □ and the larger acute angle measures □.

Explanation:

Step1: Set up variables

Let the measure of the smaller acute angle be \(x\). Then the measure of the larger acute angle is \(8x\).

Step2: Use the angle - sum property of a right - triangle

In a right - triangle, the sum of the two acute angles is \(90^{\circ}\). So, \(x + 8x=90\).

Step3: Solve the equation

Combine like terms: \(9x = 90\). Divide both sides by 9: \(x=\frac{90}{9}=10\).

Step4: Find the measure of the larger acute angle

If \(x = 10\), then the larger acute angle \(8x=8\times10 = 80\).

Answer:

The smaller acute angle measures \(10^{\circ}\) and the larger acute angle measures \(80^{\circ}\).