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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.

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lublana

Answer:

26 degree

Step-by-step explanation:

We are given that  in triangle

[tex]\angle NLM=(x+1)^{\circ}[/tex]

[tex]\angke LMN=(x+15)^{\circ}[/tex]

[tex]\angle MNO=(4x+6)^{\circ}[/tex]

[tex]\angle MNO+\angle MNL=180^{\circ}[/tex]

By using linear pair angles property

[tex]\angle MNL=180-\angle MNO=180-(4x+6)[/tex]

[tex]\angle MNL+\angle NLM+\angle LMN=180^{\circ}[/tex]

By using triangle angles sum property

[tex]180-(4x+6)+x+15+x+1=180[/tex]

[tex]2x+16=180-180+4x+6[/tex]

[tex]16-6=4x-2x=2x[/tex]

[tex]2x=10[/tex]

[tex]x=\frac{10}{2}=5[/tex]

Substitute the value

[tex]\angle MNO=4(5)+6=20+6=26^{\circ}[/tex]

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