Ask Question
7 March, 07:05

The larger of two complementary angles is 12 more than 5 times the measure of the other. Find the measures of the two angles.

+1
Answers (2)
  1. 7 March, 07:54
    0
    We know that a complementary angle is a part of angles that adds up to a total of 90 degrees. Given there are two angle measures to be deduced here, and that we have two pieces of information, this is a system of equations. We know that the smaller of the angles (angle a) and the larger of the angles (angle b) add up to a total of 90 degrees. Given this information, we can write our first equation.

    a+b=90

    We also know that angle a, the larger of the two is 12 more than five times the measure of angle b. Given this information we can write our second equation.

    a=5b+12

    Now we have to isolate for a variable in our first equation.

    a+b=90

    a=90-b

    Now we can substitute 90-b in for a in our second equation

    90-b=5b+12

    90=6b+12

    78=6b

    13=b

    b=13

    Now we can substitute the measure of b back in to our first equation to get our second answer.

    a+b=90

    a+13=90

    a=77

    We now know that using our knowledge of systems of equations, the measures of these angles are 13 and 77 degrees.
  2. 7 March, 11:00
    0
    The two angles are 77&13
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The larger of two complementary angles is 12 more than 5 times the measure of the other. Find the measures of the two angles. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers