Question

what is the ( mangle acb )? ( 10^{circ} ) ( 50^{circ} ) ( 90^{circ} ) ( 180^{circ} )

Explanation:

Step1: Use the triangle angle - sum property

In a right - triangle \( \triangle ABC\) (since there is a right - angle at \(A\)), the sum of the interior angles is \(180^{\circ}\). So, \(90^{\circ}+(4x)^{\circ}+(7x - 20)^{\circ}=180^{\circ}\).

Step2: Simplify the equation

Combine like terms: \(90 + 4x+7x - 20=180\).
\(11x+70 = 180\).
Subtract \(70\) from both sides: \(11x=180 - 70\).
\(11x = 110\).
Divide both sides by \(11\): \(x=\frac{110}{11}=10\).

Step3: Find \(m\angle ACB\)

Substitute \(x = 10\) into the expression for \(\angle ACB=(7x - 20)^{\circ}\).
\(7\times10-20=70 - 20=50^{\circ}\).

Answer:

\(50^{\circ}\)