Question

Ray QM is the angle bisector of angle NQR. If angle PQN = 7x + 15 and angle NQM = 4x, what is the value of x?

Answer 1

Answer:

x = 2.7

Step-by-step explanation:

From the question given above, the following data were obtained:

QM = angle bisector of angle PQR

Angle PQN = 7x + 15

Angle NQM = 4x

x =?

Since QM is the angular bisector, it means that it bisect PQR into two equal angle i.e 45° each.

See attachment for diagram.

Thus, we can obtain the value of x as follow:

7x + 15 + 4x + 45= 90° (angle in a right angle triangle)

7x + 4x + 15 + 45= 90

11x + 60 = 90

Collect like terms

11x = 90 – 60

11x = 30

Divide both side by 11

x = 30/11

x = 2.7

Therefore, the value of x is 2.7