15
QuizMultiple Choice

Similarity, Right Triangle Trigonometry, and Proof: Part One — Test

Question 15 • Mathematics II

Triangle JKL is isosceles. The measure of angle cap j is 72 degrees and the measure of angle cap k is 36 degrees Which statement describes angle cap l ?

Answer
A
Angle cap l is a base angle and measures 72 degrees .
B
Angle cap l is a base angle and measures 36 degrees .
C
Angle cap l is a vertex angle and measures 36 degrees .
D
Angle cap l is a vertex angle and measures 72 degrees .

Explanation

The angles in a triangle add to 180°, so angle L = 180° − 72° − 36° = 72°. Since angles J and L are equal, they are the base angles of the isosceles triangle; angle K, at the vertex between the equal sides, is 36°. Therefore, angle L is a base angle measuring 72°.

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