SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 84.75 degrees. Find the measures of the angles. What is the meas

Algebra ->  Angles -> SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 84.75 degrees. Find the measures of the angles. What is the meas      Log On


   



Question 312126: Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 84.75 degrees.
Find the measures of the angles.
What is the measure of the smaller angle ______degrees
What is the measure of the other angle ________degrees

Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
Complementary angles add up to 90 degrees.
Let's call the first angle x,
and the second angle y.
(eq1) +x+%2B+y+=+90+
We need to express the statement as an equation:
The sum of the measure of the first angle and one-fourth the second angle is 84.75 degrees:
(eq2) +x+%2B+y+%2F+4++=+84.75+
We can rewrite (eq1) as +x+=+90+-+y and then substitute into (eq2):
+x+%2B+y+%2F+4++=+%2890+-+y%29+%2B+y%2F4+
90+-+3y%2F4+=+84.75
Then +3y+%2F+4+=+5.25+, so +y+=+5.25+%2A+4+%2F+3+=+7 and x=83.
I hope that helps.