Question

In the diagram at the

right, m LMN = 116,
M JKM = 122, and
M JNM = 103. What is
m NKM?

Answer 1

77 Degrees

Explanation:

Let ∠LMK=x

Hence ∠NMK=x (Given)

Also given that ∠ NML=116

And

∠ NML=∠ LMK+∠ NMK

Hence

x+x=116

2x=116

x=58

Let ∠ MNK=y

Given ∠JNK=∠ NMK=x

Also ∠ JNM=103

x+y=103

58+y=103

y=45

Now we have ∠ JKM=122

y+∠ NKM=122

Hence

45+∠ NKM=122

∠ NKM=122-45

∠ NKM=77

Hence ∠ NKM=77