Question

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°.

Explanation:

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle J = 72^{\circ}\), \(\angle K=36^{\circ}\), and \(\angle L=x\). Then \(72 + 36+x=180\).

Step2: Solve for \(x\)

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Step3: Determine if it is a base or vertex angle

In an isosceles triangle, if two angles are equal, they are base angles. Since \(\angle J=\angle L = 72^{\circ}\), \(\angle L\) is a base angle.

Answer:

Angle L is a base angle and measures \(72^{\circ}\).