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

Question

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°.

Answer 1

In triangle JKL, we know that it is isosceles. This means two of its angles are equal. The given measures are:

• Angle J = 72°
• Angle K = 36°

Since the sum of the angles in any triangle is 180°, we can calculate angle L:

\[ \text{Angle L} = 180° - \text{Angle J} - \text{Angle K} = 180° - 72° - 36° = 72° \]

Now, since angle L measures 72° and angle J also measures 72°, angles J and L are equal, and therefore they are the base angles of the isosceles triangle, while angle K (36°) is the vertex angle.

Thus, the correct statement about angle L is:

Angle L is a base angle and measures 72°.