THIS USER ASKED 👇

Triangle KNM is isosceles, where angle N is the vertex.

What is the measure of angle K?
0110
N
25°
50°
(5x +10) (6x – 1)
65°
K
L
M

THIS IS THE BEST ANSWER 👇

Measure angle K = 25 °.

Step by step explanation:

ΔKNM is called an isosceles triangle with KL = LM and ∠K = ∠M, so NL bisects ∠KNM.

∠KNL = ∠LNM

⇒5x + 10 = 6x-1

⇒x = 11 °

So ∠KNM = ∠KNL + ∠LNM

∠KNM = 5x + 10 + 6x-1 = 11x + 9 = 11 (11) + 9 = 130 °

Now, Since, an isosceles triangle with KL = LM and ∠K = ∠M, ∠K = ∠M, using the property of the angle sum in ΔKNM, and NL bisects ∠KNM, so we find

∠NKM + ∠KNM + ∠KMN = 180 °

⇒2∠NKM + 130 ° = 180 °

⇒2∠NKM = 50 °

⇒∠NKM = 25 °

Therefore, measure angle K = 25 °.