Question

In ΔMNO, \overline{MO}

MO

is extended through point O to point P, \text{m}\angle MNO = (3x+11)^{\circ}m∠MNO=(3x+11)

∘

, \text{m}\angle OMN = (2x+20)^{\circ}m∠OMN=(2x+20)

∘

, and \text{m}\angle NOP = (8x-5)^{\circ}m∠NOP=(8x−5)

∘

. What is the value of x?x?

Answer 1

Answer: x=12

Explanation:

Answer 2

x = 12

Explanation:

Given the triangle MNO which is extended through point O to point P, we are given the followings;

Interior angles;

∠MNO=(3x+11)

∠OMN=(2x+20)

Exterior angle;

∠NOP=(8x−5)

To find x, we will use the theorem, "The sum of the interior angles is equal to the exterior"

Hence;

3x+11+2x+20 = 8x - 5

5x + 31 = 8x - 5

Collect like terms;

5x - 8x = -5-31

-3x = -36

x = -36/-3

x = 12

Hence the value of x is 12