EREIDHAS MATH Mhautad \#17 Chech Usten 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 \( \square \) \( { }^{\circ} \) and the larger acute angle measures \( \square \)。

To solve the problem, we need to find the measures of the two acute angles in a right triangle, where one angle is 8 times the measure of the other. ### Step 1: Define the angles Let: - \( x \) = measure of the smaller acute angle (in degrees) - \( 8x \) = measure of the larger acute angle (in degrees) ### Step 2: Use the triangle angle sum property In a right triangle, the sum of the two acute angles is \( 90^\circ \). Therefore, we can set up the equation: \[ x + 8x = 90 \] ### Step 3: Simplify the equation Combine like terms: \[ 9x = 90 \] ### Step 4: Solve for \( x \) Now, divide both sides by 9: \[ x = \frac{90}{9} = 10 \] ### Step 5: Find the larger angle Now that we have \( x \), we can find the larger angle: \[ 8x = 8 \times 10 = 80 \] ### Conclusion The measures of the angles are: - The smaller acute angle measures \( 10^\circ \). - The larger acute angle measures \( 80^\circ \). Thus, the final answer is: - The smaller acute angle measures \( 10^\circ \) and the larger acute angle measures \( 80^\circ \).