SOLUTION: Use the five steps for problem solving to answer the following question. Please show all of your work. Angle P and Angle Q are supplementary angles. If Angle Q is ten less than

Algebra ->  Angles -> SOLUTION: Use the five steps for problem solving to answer the following question. Please show all of your work. Angle P and Angle Q are supplementary angles. If Angle Q is ten less than       Log On


   

Question 482547: Use the five steps for problem solving to answer the following question. Please show all of your work.
Angle P and Angle Q are supplementary angles. If Angle Q is ten less than four times Angle P, what are the measures of the angles?
Found 2 solutions by cleomenius, MathTherapy:
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
p + q = 180
q = 4p + 10
Next, I substitute into the first equation.
p + 4p + 10 = 180
5p = 170
p = 34
4(34) + 10 + 34 =180
136 + 10 + 34 = 180, checks
Cleomenius.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Since angles P & Q are supplementary, then P + Q = 180

Since angle Q is 10 less than 4 times angle P, then we can say that: Q = 4P – 10 ------ - 4P + Q = - 10

P + Q = 180 -------- eq (i)
– 4P + Q = - 10 --------- eq (ii)
4P + 4Q = 720 ------- eq (iii) -------- Multiplying eq (i) by 4
5Q = 710 ------ Adding eq (ii) and (iii)
Angle Q = 710%2F5 = highlight_green%28142%5Eo%29

Substituting 142 for Q in eq (i) results in: P + 142 = 180

Angle P = 180 – 142 = highlight_green%2838%5E0%29

------------
Check
------------
Angle Q = 142%5Eo
Angle P = 38%5Eo, so 4 times angle P = 4 * 38 = 152%5Eo

It can be seen that angle Q (142%5Eo) is 10 less than 4 times angle P (152%5Eo)

Send comments and “thank-yous” to MathMadEzy@aol.com