In ΔJKL, m∠J = 83° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
a) 7°
b) 86.5°
c) 97°
d) 173°
The sum of the measures of the interior angles of a triangle is always 180°.
Therefore, m∠J + m∠K + m∠L = 180°
We know that m∠J = 83° and m∠L = 90°.
Substituting these values into the equation, we get:
83° + m∠K + 90° = 180°
Combining like terms, we get:
173° + m∠K = 180°
Subtracting 173° from both sides, we get:
m∠K = 7°
Since the question asks for the measure of the exterior angle to ∠K, we subtract 7° from 180° to find the measure of the exterior angle:
180° - 7° = 173°
Therefore, the measure of the exterior angle to ∠K is 173°.
The correct answer is d) 173°.