Question

In ΔMNO, \text{m}\angle M = (6x+1)^{\circ}m∠M=(6x+1) ∘ , \text{m}\angle N = (3x-10)^{\circ}m∠N=(3x−10) ∘ , and \text{m}\angle O = (x+19)^{\circ}m∠O=(x+19) ∘ . Find \text{m}\angle N.m∠N.

Answer 1

Applying the triangle sum theorem, m∠N = 41°

What is the Triangle Sum Theorem?

Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.

Given the following interior angles of ΔMNO:

m∠M = (6x+1)°

m∠N = (3x-10)°

m∠O = (x+19)°

Find the value of x:

m∠M + m∠N + m∠O = 180°

• Substitute

6x+1 + 3x-10 + x+19 = 180

• Add like terms

10x + 10 = 180

10x = 180 - 10

10x = 170

• Divide both sides by 10

x = 17

m∠N = (3x-10)°

• Plug in the value of x

m∠N = 3(17) - 10

m∠N = 41°

Learn more about triangle sum theorem on:

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