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 angle - sum property of a triangle

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

Step2: Substitute the given angle measures

We know \(m\angle J = 72^{\circ}\) and \(m\angle K = 36^{\circ}\). Substituting these values into the equation \(72^{\circ}+36^{\circ}+m\angle L = 180^{\circ}\).

Step3: Solve for \(m\angle L\)

First, add 72° and 36°: \(72^{\circ}+36^{\circ}=108^{\circ}\). Then the equation becomes \(108^{\circ}+m\angle L = 180^{\circ}\). Subtract 108° from both sides: \(m\angle L=180^{\circ}- 108^{\circ}=72^{\circ}\).

Step4: Determine the type of angle

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

Answer:

Angle L is a base angle and measures 72°.