Question

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

a. 7 degrees
b. 13 degrees
c. 43 degrees
d. 48 degrees

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 setting up an equation and solving for x, we can find the value of angle PQR.

Step-by-step explanation:

To find the measure of angle PQR, we need to use the fact that the sum of the angles in a triangle is 180 degrees. First, let's write an equation using the given angles:

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

Combine like terms:

10x - 6 = 180

Add 6 to both sides:

10x = 186

Divide both sides by 10:

x = 18.6

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

m∠PQR = (7x - 19) = (7(18.6) - 19) = 130.2 - 19 = 111.2 degrees

Therefore, the measure of angle PQR is approximately 111.2 degrees (rounded to one decimal place).