Question

△JKL and △LMN are shown.

There are two triangles, triangle JKL and triangle LMN with common vertex L. The angle KLJ and angle NLM are opposite angles. Side JK is congruent to side KL. Side LN is congruent to side LM. The measure of angle JKL is 72⁰.
What is m∠KJL?
m∠KJL = ˚

Answer 1

The measure of angle KJL in an isosceles triangle JKL with sides JK and KL congruent and angle JKL as 72° is calculated to be 54°.

Step-by-step explanation:

In geometry, if triangle JKL has sides JK and KL congruent, then it is an isosceles triangle, with angles JKL and KJL being the base angles which must be equal. Since the measure of angle JKL is given as 72°, we can find the measure of angle KJL using the fact that the sum of angles in any triangle is 180°. We calculate m∠KJL as follows:

1. Sum of angles in △JKL = m∠JKL + m∠KLJ + m∠KJL = 180°.
2. Since JK ≃ KL, △JKL is isosceles, so m∠JKL = m∠KJL.
3. Let m∠KJL = y degrees. Therefore, 72° + y + y = 180°.
4. Combine like terms: 72° + 2y = 180°.
5. Subtract 72 degrees from both sides: 2y = 108°.
6. Divide both sides by 2: y = 54°.

Thus, the measure of angle KJL (m∠KJL) is 54°.