Question

if (\triangle tap=\triangle xzp) what is the measure of (angle p)?
(mangle p=)

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle TAP\cong\triangle XZP\), corresponding angles are equal. In a triangle, the sum of interior angles is \(180^{\circ}\).

Step2: Calculate \(\angle P\)

We know that for \(\triangle TAP\), \(\angle A = 96^{\circ}\) (corresponds to \(\angle Z\) in \(\triangle XZP\)), and if we assume we are using the angle - sum formula for a triangle \(A + X+P=180^{\circ}\) (where \(X = 56^{\circ}\)). Then \(P=180^{\circ}-(96^{\circ}+ 56^{\circ})\).

$$P = 180^{\circ}-152^{\circ}=28^{\circ}$$

Answer:

\(28^{\circ}\)