Question

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

Explanation:

Step1: Use triangle angle - sum property

In \(\triangle ABC\), \(\angle A = 90^{\circ}\), \(\angle B=(4x)^{\circ}\), \(\angle C=(7x - 20)^{\circ}\).
By the triangle angle - sum property \(\angle A+\angle B+\angle C = 180^{\circ}\).
So, \(90+(4x)+(7x - 20)=180\).

Step2: Simplify the equation

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

Step3: Find \(\angle ACB\)

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

Answer:

B. \(50^{\circ}\)