Question

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

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

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:

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