Question

The measure of ∠JLM is 140°. The measure of ∠JKL is 75°. What is the measure of ∠KJL? Enter your answer in the box. ° A triangle J K L. Side K L is the base. A ray extends through vertex L in horizontal direction and passes through a point labeled as M.

Answer 1

∠KJL is 65

Explanation:

∠JLM + ∠JLK = 180°

140° + ∠JLK = 180°

∠JLK = 180° - 140°

∠JLK = 40°

∠JLK + ∠JKL + ∠KJL = 180°

75° + 40° + ∠KJL = 180°

115° + ∠KJL = 180°

∠KJL = 180° - 115°

∠KJL = 65°

Answer 2

65 degrees

Explanation:

Given that JKL is a triangle. One of the angles JKL is 75 degrees. The base is KL and it is extended to M.

The angle JLM is 140 degrees is given.

Note that angle JLM is the exterior angle of the triangle JKL.

By properties of triangles we have

Exterior angle of a triangle = sum of other two interior angles.

Use this to find KJL.

Since JLM is exterior angle and other two interior are JKL and KJL we get

angle JKL + angle KJL = angle JLM

Substitute the known values

75+angle KJL = 140

Subtract 75

Angle KJL = 140-75 = 65 degrees