Question

what is the m∠acb? a right - angled triangle at a, angle at b is (4x)°, angle at c is (7x - 20)°. options: 10°, 50°, 90°, 180°

Explanation:

Step1: Recall triangle angle sum

In a right triangle, the sum of angles is \(180^\circ\), and one angle is \(90^\circ\). So \(90 + 4x + 7x - 20 = 180\).

Step2: Simplify the equation

Combine like terms: \(70 + 11x = 180\). Subtract 70: \(11x = 110\). Divide by 11: \(x = 10\).

Step3: Find \(m\angle ACB\)

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

Answer:

\(50^\circ\) (corresponding to the option "50°")