Question

what is the m∠acb?
○ 10°
○ 50°
○ 90°
○ 180°
(diagram: triangle abc with right angle at a, ∠b = (4x)°, ∠c = (7x - 20)°)

Explanation:

Step1: Recall triangle angle sum

In a triangle, the sum of angles is \(180^\circ\). Since \(\angle A = 90^\circ\), we have \(90 + 4x + (7x - 20) = 180\).

Step2: Simplify the equation

Combine like terms: \(90 - 20 + 4x + 7x = 180\) → \(70 + 11x = 180\).

Step3: Solve for x

Subtract 70: \(11x = 180 - 70 = 110\) → \(x = \frac{110}{11} = 10\).

Step4: Find \(m\angle ACB\)

Substitute \(x = 10\) into \(7x - 20\): \(7(10) - 20 = 70 - 20 = 50\).

Answer:

\(50^\circ\)