Question

if the m∠2 = 42°, what is the m∠1?

Explanation:

Step1: Identify the triangle type

The triangle is isosceles (two equal - length sides), so the base angles are equal. Let the base angles be \(x\).

Step2: Use the exterior - angle theorem

The exterior angle (\(\angle1\)) of a triangle is equal to the sum of the two non - adjacent interior angles. In an isosceles triangle with \(\angle2 = 42^{\circ}\), the two non - adjacent interior angles are equal (because of the isosceles property). So, \(m\angle1=2\times m\angle2\).

Answer:

\(84^{\circ}\) (Since \(m\angle1 = 2\times42^{\circ}=84^{\circ}\), but this is not among the given options. There might be a mis - understanding. If we use the exterior - angle formula \(m\angle1=m\angle2 + m\) (the other non - adjacent interior angle). Since the triangle is isosceles, the other non - adjacent interior angle is equal to \(\angle2\). So \(m\angle1 = 42^{\circ}+42^{\circ}=84^{\circ}\). But if we assume a wrong approach (maybe a one - step wrong addition), if we consider \(m\angle1=42^{\circ}+ 69^{\circ}\) (no geometric basis), it's wrong. If we use the formula \(m\angle1 = 180^{\circ}-(180 - 2\times42)^{\circ}\) (using the linear pair and triangle angle - sum), \(m\angle1=84^{\circ}\). But among the options, if there is a mistake in the problem's options, perhaps the intended answer is \(69^{\circ}\) (but this is incorrect geometrically. The correct geometric answer is \(84^{\circ}\), but if we assume a wrong step like \(m\angle1=180-(180 - 42 - 69)\) (no basis), it's wrong. The proper geometric answer using the exterior - angle theorem for an isosceles triangle: \(m\angle1 = 2\times42^{\circ}=84^{\circ}\))