Question

1. find ∠4 if △xyz is not regular but ∠1 = 40° and m∠2 = 35°.

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In \(\triangle XYZ\), if we assume \(\angle1\), \(\angle2\) and \(\angle4\) are the interior angles of the triangle, then \(\angle1+\angle2 + \angle4=180^{\circ}\).

Step2: Solve for \(\angle4\)

We can rewrite the equation as \(\angle4 = 180^{\circ}-\angle1-\angle2\). Substitute \(\angle1 = 40^{\circ}\) and \(\angle2=35^{\circ}\) into the equation. So \(\angle4=180 - 40-35\).
\(\angle4 = 105^{\circ}\)

Answer:

\(105^{\circ}\)