In triangle klm, if k is congruent to l, kl = 9x - 40, lm = 7x - 37, & km = 3x + 23, find x & the measure of each angle.

x=15, ∠L=∠K=45.7° and ∠M is 77.6°.

Step-by-step explanation:

Given information: ∠L≅∠K, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23.

Two angles are congruent, so triangle KLM is an isosceles triangle. Corresponding adjacent sides of congruent angles are equal.

The sides KM and LM are congruent.

Isolate variable terms.

Divide both sides by -4.

The value of x is 15.

The length of sides of triangle KLM are

Therefore length of sides are 68, 68 and 95.

Law of cosine

Using the above formula we get

Therefore, ∠L=∠K=45.7° and ∠M is 77.6°.

answer: the answer is 127 degrees

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step-by-step explanation: