Questions: What is the measure of angle MJK in the figure below? A. 58° B. 64° C. 32° D. 60° E. 15° F. Cannot be determined

What is the measure of angle MJK in the figure below? A. 58° B. 64° C. 32° D. 60° E. 15° F. Cannot be determined
Transcript text: 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
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Solution

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Solution Steps

Step 1: Analyze the given information

Triangle SJK is an isosceles triangle because SJ = JK = 7. Angle MSJ is 90 degrees, and angle SJM is given as 32 degrees. Angle JKS is also 90 degrees.

Step 2: Find angle JSJ

Since the sum of angles in a triangle is 180 degrees, the angle JSK in triangle SJK is given by: Angle JSK = 180 - (angle SJK + angle JKS) = 180 - (32 + angle JKS). Since triangle SJK is isosceles with SJ = JK, the base angles SJK and JKS are equal. Let x be the measure of angle SJK and angle JKS. Then, 2x + 32 = 180. 2x = 180 - 32 2x = 148 x = 74 So, angle SJK = angle JKS = 74 degrees.

Step 3: Find angle MJK

Angle MJK = Angle MJS + Angle SJK. Since Angle MJS = 90 degrees and Angle SJK = 74 degrees, Angle MJK = 90 + 74 = 164 degrees.

Step 4: Find angle MJK

Angle MJK = Angle MJS + Angle SJK Since Angle MJS is a right angle (90 degrees) and Angle JKS is 74 degrees, angle MJK is MJK = Angle MJS - Angle JKS = 90 - 74 = 16. Since angle KJL = 90 degrees and angle JKL = 74 degrees, angle JLK = 180 - 90 - 74 = 16 degrees. Angle SJK = 74 degrees. Angle MJK = Angle MJS + Angle SJK = 90 + 74 = 164 degrees. Angle MJN = 180 - 164 = 16 degrees. Angle MJK = Angle MJS - Angle KJS Angle MJK = 90 - 74 Angle MJK = 16

Final Answer

\\(\boxed{16^{\circ}}\\)

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