Question

in △abc, ∠c = 50° if ∠a ≅ ∠b find the measure of each angle
∠a =
∠b =

Explanation:

Step1: Recall triangle angle sum property

The sum of the interior angles of a triangle is \(180^\circ\). So, in \(\triangle ABC\), we have \(\angle A+\angle B+\angle C = 180^\circ\).

Step2: Substitute known values and equal angles

We know \(\angle C = 50^\circ\) and \(\angle A\cong\angle B\) (so \(\angle A=\angle B\)). Let \(\angle A = \angle B=x\). Then the equation becomes \(x + x+ 50^\circ=180^\circ\).

Step3: Solve for \(x\)

Combine like terms: \(2x+50^\circ = 180^\circ\). Subtract \(50^\circ\) from both sides: \(2x=180^\circ - 50^\circ=130^\circ\). Divide both sides by 2: \(x=\frac{130^\circ}{2} = 65^\circ\).

Answer:

\(\angle A = 65^\circ\), \(\angle B = 65^\circ\)