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: Calculate \(m\angle L\)

Substitute \(m\angle J = 72^\circ\) and \(m\angle K = 36^\circ\) into the formula:
\(72^\circ + 36^\circ + m\angle L = 180^\circ\)
\(108^\circ + m\angle L = 180^\circ\)
\(m\angle L = 180^\circ - 108^\circ = 72^\circ\).

Step3: Identify base/vertex angles

In an isosceles triangle, base angles are equal. Here, \(m\angle J = m\angle L = 72^\circ\), so they are base angles (the vertex angle would be the unequal one, \(m\angle K = 36^\circ\)).

Answer:

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