Question

In ΔOPQ. overline OQ is extended through point Q to point R, m∠ PQR=(7x-19) m∠ OPQ=(2x-3)° ,and m∠ QOP=(x-16)° . Find m∠ PQR

Answer 1

To find the measure of angle PQR, we can use the fact that the sum of the angles in a triangle is 180 degrees. By substituting the given expressions for the angles in the equation and solving for x, we can find the value of x and then calculate the measure of angle PQR.

Step-by-step explanation:

To find the measure of angle PQR, we can use the fact that the sum of the angles in a triangle is 180 degrees. So we have:

(7x-19) + (2x-3) + (x-16) = 180

Simplifying the equation, we get:

10x - 38 = 180

Adding 38 to both sides and solving for x, we get:

10x = 218

x = 21.8

Now we can substitute the value of x back into the equation for angle PQR:

(7(21.8) - 19) = 130.6 degrees