Question

if the m∠2 = 42°, what is the m∠1?

Explanation:

Step1: Use the property of exterior angles

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In this case, \(\angle1\) is an exterior angle of the isosceles triangle (since two sides are equal), and the non - adjacent interior angle is \(\angle2\). Let the other non - adjacent interior angle (equal to the angle opposite the equal side) also be equal to \(\angle2\) (because the triangle has two equal sides, so the base angles are equal).

Step2: Calculate \(\angle1\)

According to the exterior angle formula \(\angle1=\angle2 + \angle2\) (since the two non - adjacent interior angles are equal). Given \(\angle2 = 42^{\circ}\), then \(\angle1=42^{\circ}+42^{\circ}\)

Answer:

\(84^{\circ}\) (It seems there might be a mistake in the provided options as the correct calculation gives \(84^{\circ}\) based on the exterior angle property of a triangle where the two non - adjacent interior angles are equal (due to the triangle having two equal sides). If we assume a different property (maybe a mis - drawn figure), but strictly by the exterior angle theorem for a triangle with two equal non - adjacent interior angles (from the equal sides), the answer should be \(84^{\circ}\))