Question

In ΔLMN, \overline{LN} LN is extended through point N to point O, m∠NLM = (x+1)^{\circ}(x+1) ∘ , m∠LMN = (x+15)^{\circ}(x+15) ∘ , and m∠MNO = (4x+6)^{\circ}(4x+6) ∘ . Find m∠MNO.

Answer 1

26 degree

Explanation:

We are given that in triangle

`\angle NLM=(x+1)^(\circ)`

`\angke LMN=(x+15)^(\circ)`

`\angle MNO=(4x+6)^(\circ)`

`\angle MNO+\angle MNL=180^(\circ)`

By using linear pair angles property

`\angle MNL=180-\angle MNO=180-(4x+6)`

`\angle MNL+\angle NLM+\angle LMN=180^(\circ)`

By using triangle angles sum property

`180-(4x+6)+x+15+x+1=180`

`2x+16=180-180+4x+6`

`16-6=4x-2x=2x`

`2x=10`

`x=(10)/(2)=5`

Substitute the value

`\angle MNO=4(5)+6=20+6=26^(\circ)`