Final answer:
To find the exterior angle to ∠K in ΔJKL with angles J and L given as 67° and 90°, respectively, we first find ∠K as 23°. However, the exterior angle calculation leads to 157°, which is not listed in the options, indicating a potential typo in the question. If the question is about the exterior angle to ∠J, the correct answer is likely option (d) 113°.
Step-by-step explanation:
The student is asked to determine the measure of the exterior angle to ∠K in ΔJKL, where m∠J is 67° and m∠L is 90°. To find this, we first need to calculate the measure of ∠K itself. Since the sum of all angles in a triangle is 180°, we can write the equation:
m∠J + m∠K + m∠L = 180°
Substitute the given angle measures into the equation:
67° + m∠K + 90° = 180°
This simplifies to m∠K = 180° - 67° - 90°, which gives us m∠K = 23°. Since an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles, the measure of the exterior angle to ∠K is:
m∠J + m∠L = 67° + 90° = 157°
However, the options provided in the question do not include 157°, so there might be a mistake in the question. If we consider the possibility of a typo, and they meant the exterior angle to ∠J or ∠L, then for ∠L, being a right angle, its exterior angle would be 90°, and for ∠J, it would be 180° - 67° = 113°, which is option (d). If the exterior angle in question is indeed for ∠K as stated, none of the given options are correct. Therefore, based on the provided information, the most likely correct answer is option (d) 113°, assuming the student meant the exterior angle to ∠J.