Question

find the measure of the indicated angles.
complementary angles with measures 3x - 7 and 6x - 11

the angles are
(simplify your answer. type an integer or a fraction. type your answer in degrees. do not include the degree symbol in your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Recall complementary angles sum to 90°

Complementary angles add up to \( 90^\circ \), so we set up the equation: \( (3x - 7) + (6x - 11) = 90 \)

Step2: Combine like terms

Simplify the left side: \( 3x + 6x - 7 - 11 = 90 \) which becomes \( 9x - 18 = 90 \)

Step3: Solve for x

Add 18 to both sides: \( 9x = 90 + 18 \) so \( 9x = 108 \). Then divide by 9: \( x = \frac{108}{9} = 12 \)

Step4: Find each angle

First angle: \( 3x - 7 = 3(12) - 7 = 36 - 7 = 29 \)
Second angle: \( 6x - 11 = 6(12) - 11 = 72 - 11 = 61 \)

Answer:

29, 61