Question

you only have 5 questions left to raise your score. question find ( mangle pon ).

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle PON \) is isosceles because \( PO = PN \). In an isosceles triangle, the base - angles are equal. Let \( \angle O=\angle N = x\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \( 180^{\circ}\). So, \( \angle P+\angle O+\angle N = 180^{\circ}\). Given \( \angle P = 36^{\circ}\), and \( \angle O=\angle N \), we have \( 36^{\circ}+x + x=180^{\circ}\).

Step3: Solve for \( x\)

Combine like terms: \( 36^{\circ}+2x=180^{\circ}\). Subtract \( 36^{\circ}\) from both sides: \( 2x=180^{\circ}- 36^{\circ}=144^{\circ}\). Divide by 2: \( x = 72^{\circ}\). But wait, we made a mistake. Wait, no, actually, if \( PO = PN\), then \( \angle O=\angle N\). Wait, no, the problem is to find \( \angle PON\). Wait, no, the triangle \( \triangle PON\) with \( PO = PN\), so \( \angle O=\angle N\). Using the angle - sum formula \( \angle P+\angle O+\angle N=180^{\circ}\), substituting \( \angle P = 36^{\circ}\), we get \( 36^{\circ}+2\angle O=180^{\circ}\). Then \( 2\angle O=144^{\circ}\), \( \angle O = 108^{\circ}\).

Answer:

\(108^{\circ}\)