Question

a triangle has two angles that measure $37^{circ}$ and $25^{circ}$.
lewis states that the measure of the exterior angle of the unknown angle is $62^{circ}$, while andrew states that the measure of the exterior angle is $75^{circ}$.
who is correct? explain your reasoning
show hints

• neither person is correct. the sum of the two given angle measures is $37^{circ}+25^{circ}=62^{circ}$, so the measure of the exterior angle of the unknown angle
• lewis is correct. the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
• andrew is correct. an exterior angle of a triangle is supplementary to the smaller of its two remote interior angles.
• they are both correct. there are two ways to draw an exterior angle of the unknown angle. one way yields an exterior angle that measures $62^{circ}$. the

Explanation:

Step1: Recall the exterior angle theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Step2: Calculate the sum of the given angles

The two given angles are \(37^{\circ}\) and \(25^{\circ}\). Their sum is \(37^{\circ}+ 25^{\circ}=62^{\circ}\).

Answer:

Leah is correct. The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.