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˚.
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