Complementary angles are two angles that have measures with a sum of 90°. Angles P and Q are complementary and the measure of angle P is 6° more than twice the measure of angle Q.Write a system of equations and use substitution to find the measures of angles P and Q.
Input Field 1 of 1
Answers
Answer:
P = 62° Q = 28°
Step-by-step explanation:
Let x = measure of angle Q
then y = measure of angle P
Now x + y = 90 and 2x + 6 = y
Substituting 2x + 6 from the second equation in for y in the first equation, we get x + 2x + 6 = 90 since the two angles are complementary.
3x + 6 = 90
3x = 84
x = 28
y = 2(28) + 6 = 56 + 6 = 62
Check: 28 + 62 = 90
Final answer:
To find the measures of complementary angles P and Q, we set up a system of equations based on the problem's information, solve for one variable, then substitute that variable's value into the other equation. After solving, we find that the measure of angle P is 62°, and the measure of angle Q is 28°.
Explanation:
Let's denote the measure of angle Q as 'q'. Therefore, the measure of angle P can be expressed as '2q + 6'. Now, we can set up two equations based on the information given:
- P + Q = 90°, or in terms of 'q', (2q + 6) + q = 90°
- P = 2Q + 6°, or in terms of 'q', (2q + 6) = 2q + 6
Solving the first equation gives us 3q + 6 = 90. Subtract 6 from each side of the equation to get 3q = 84. Divide each side by 3 to solve for 'q', and we find that q = 28°. Substituting q = 28° into equation 2, we find that P = 2*28 + 6 = 62°. So, angle P is 62° and angle Q is 28°.
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