The QM beam passes between the sides of the CQF angle equal to 69 °.

The QM beam passes between the sides of the CQF angle equal to 69 °. Find the MQC and MQF angles if the MQC angle is 27 ° greater than the MQF angle

1. Let’s denote the degree measure of the angle MQF by x.

2. Let’s define the degree measure of the angle MQС:

(x + 27˚).

3. Since the angle CQF = angle MQF + angle MQC, compose and solve the equation:

(x + 27˚) + x = 69˚;

x + 27˚ + x = 69˚;

2x + 27˚ = 69˚;

2x = 69˚ – 27˚;

2x = 42˚;

x = 42˚: 2;

x = 21˚.

4. The degree measure of the angle MQF is x = 21˚.

5. What is the degree measure of the MQC angle?

x + 27˚ = 21˚ + 27˚ = 48˚.

Answer: the degree measures of the angles MQF and MQC are equal to 21˚ and 48˚.