Question

question 5 of 10
what is the measure of \\( \angle m j k \\) in the figure below?
a. \\( 58 ^ { \circ } \\)
b. \\( 64 ^ { \circ } \\)
c. \\( 32 ^ { \circ } \\)
d. \\( 60 ^ { \circ } \\)
e. \\( 15 ^ { \circ } \\)
f. cannot be determined

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(JM = JK = 7\), \(JL=JL\) (common side), and \(\angle JML=\angle JKL = 90^{\circ}\), by the HL - Congruence Theorem, \(\triangle JML\cong\triangle JKL\).

Step2: Use the property of congruent triangles

For congruent triangles \(\triangle JML\) and \(\triangle JKL\), \(\angle MJL=\angle KJL\). Given \(\angle MJL = 32^{\circ}\), then \(\angle MJK=\angle MJL+\angle KJL\).

Step3: Calculate \(\angle MJK\)

Substitute \(\angle MJL=\angle KJL = 32^{\circ}\) into the formula \(\angle MJK=\angle MJL+\angle KJL\). So \(\angle MJK=32^{\circ}+ 32^{\circ}=64^{\circ}\).

Answer:

B. \(64^{\circ}\)