The Two Angles Are Complementary. The Sum Of The Measure Of The First Angle And Half The Second Angle Is 81.5 Degrees. Find The Measures Of The Angles
A+B=90
A+B/2=81.5
subtract the equations
B/2=8.5 deg
then find B, then go back and find A
To solve this problem, we can set up a system of equations. Let's denote the first angle as x and the second angle as y.
Since the two angles are complementary, we know that their sum is 90 degrees:
x + y = 90
We are also given that the sum of the measure of the first angle and half the second angle is 81.5 degrees:
x + (1/2)y = 81.5
Now we can solve this system of equations using substitution or elimination method.
Substitution Method:
From the first equation, we have x = 90 - y. We can substitute this value into the second equation:
(90 - y) + (1/2)y = 81.5
Now solve for y:
90 - y + (1/2)y = 81.5
Multiply both sides by 2 to eliminate the fraction:
180 - 2y + y = 163
180 - y = 163
Subtract 180 from both sides:
-y = 163 - 180
-y = -17
Divide both sides by -1 to solve for y:
y = 17
Now substitute the value of y back into the first equation to solve for x:
x + 17 = 90
Subtract 17 from both sides:
x = 90 - 17
x = 73
Therefore, the measures of the angles are x = 73 and y = 17.