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

Answer:

26 degree

Step-by-step 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

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

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

$16-6=4x-2x=2x$

$2x=10$

$x=\frac{10}{2}=5$

Substitute the value

$\angle MNO=4(5)+6=20+6=26^{\circ}$