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 triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, for \(\triangle JKL\), \(m\angle J + m\angle K + m\angle L = 180^\circ\).

Step2: Substitute known angles

We know \(m\angle J = 72^\circ\) and \(m\angle K = 36^\circ\). Substitute these values: \(72^\circ + 36^\circ + m\angle L = 180^\circ\).

Step3: Calculate \(m\angle L\)

First, add \(72^\circ\) and \(36^\circ\): \(72^\circ + 36^\circ = 108^\circ\). Then, solve for \(m\angle L\): \(m\angle L = 180^\circ - 108^\circ = 72^\circ\).

Step4: Identify angle type (base/vertex)

In an isosceles triangle, base angles are equal. Here, \(\angle J\) and \(\angle L\) both measure \(72^\circ\), so they are base angles (the two equal angles in an isosceles triangle are base angles, and the unequal one is the vertex angle; here \(\angle K = 36^\circ\) is the vertex angle).

Answer:

Angle L is a base angle and measures \(72^\circ\). (Corresponding to the option: Angle L is a base angle and measures \(72^\circ\).)