SOLUTION: ∠PQR and ∠ABC are complementary angles and ∠PQR is four times as large as ∠ABC. Determine the measure of each angle. Students must show all work step by ste

Algebra ->  Angles -> SOLUTION: ∠PQR and ∠ABC are complementary angles and ∠PQR is four times as large as ∠ABC. Determine the measure of each angle. Students must show all work step by ste      Log On


   

Question 401345: ∠PQR and ∠ABC are complementary angles and ∠PQR is four times as large as ∠ABC. Determine the measure of each angle. Students must show all work step by step to receive full credit for the problem.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let ∠PQR = x and ∠ABC = 90 - x (we can make this assumption since they're complementary)

Then, ∠PQR = 4∠ABC --> x+=+4%2890-x%29 --> x+=+360+-+4x --> x = 72. Therefore ∠PQR = 72 and ∠ABC = 18 (degrees).