Question

In △ NOP, overline NP is extended through point P to point Q, m∠ OPQ=(9x-19)° , m∠ PNO=(2x+5)°, and m∠ NOP=(3x+16)° . Find m∠ NOP.

Answer 1

The measure of angle NOP is 54.13 degree.

Step-by-step explanation:

To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Let's set up an equation:

(3x+16) + (2x+5) + (9x-19) = 180

Simplifying the equation, we get:

14x + 2 = 180

Subtracting 2 from both sides, we have:

14x = 178

Dividing both sides by 14, we find:

x = 178/14 = 12.71

Therefore, the measure of angle NOP is:

(3x+16) = (3*12.71 + 16) = 54.13 degree