Question

solving for interior angle measures. what is the m∠acb? (4x)°. (7x - 20)°. 10°. 50°. 90°. 180°

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is 180°. In triangle ABC, we have a right - angle (90°), an angle of (4x)° and an angle of (7x - 20)°. So, 90+4x+(7x - 20)=180.

Step2: Simplify the left - hand side of the equation

Combine like terms: 90-20 + 4x+7x=180, which gives 70 + 11x=180.

Step3: Solve for x

Subtract 70 from both sides: 11x=180 - 70, so 11x=110. Then divide both sides by 11: x = 10.

Step4: Find the measure of ∠ACB

The measure of ∠ACB is (7x - 20)°. Substitute x = 10 into the expression: 7(10)-20=70 - 20=50°.

Answer:

50°