Final answer:
To find the measure of the exterior angle adjacent to ∠K in triangle ΔJKL, subtract the sum of the given angles ∠J and ∠L from 180° to get ∠K, then subtract ∠K from 180° to find the exterior angle. The measure of the exterior angle is 173°.
Step-by-step explanation:
The subject of this question is Mathematics, specifically it involves solving for the measure of an exterior angle in a triangle. We are given a triangle ΔJKL with interior angles m∠J = 83° and m∠L = 90°. To find the measure of the exterior angle adjacent to ∠K, we will use the fact that the sum of the measures of the interior angles of a triangle is always 180°. Since one angle is 90° and the other is 83°, we calculate the third angle by subtracting the sum of the given angles from 180°.
m∠K = 180° - (m∠J + m∠L) = 180° - (83° + 90°) = 180° - 173° = 7°
Now, the exterior angle adjacent to ∠K is supplementary to the interior ∠K, meaning they add up to 180°. So, the measure of the exterior angle is:
m exterior angle = 180° - m∠K = 180° - 7° = 173°.