Triangle JKL is isosceles. The measure of angle J is 72° and the measure of angle K is 36°. Which statement describes angle L?

Angle L is a base angle and measures 36°.
Angle L is a base angle and measures 72°.
Angle L is a vertex angle and measures 36°.
Angle L is a vertex angle and measures 72°.

The correct answer is option B: L is a base angle and measures 72 degrees

Step-by-step explanation: Please refer to the attached diagram for details. An isosceles triangle basically has two sides measuring the same length and two angles also having the same measurement. Based on the labeling of the triangle JKL, angle J is one point measuring 72 degrees, while angle K is another point measuring 36 degrees.

The measurement of angle L is derived as,

J + K + L = 180 {Sum of angles in a triangle equals 180}

72 + 36 + L = 180

108 + L = 180

Subtract 108 from both sides of the equation

L = 72

Angles J and L both measure 72 degrees which satisfies the condition for an isosceles triangle and they are both on the base of the triangle. The third angle is always “opposite” the two equal angles (regardless of if the triangle is rotated left or right)

step-by-step explanation:

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