two angles are complementary. the sum of the measure of the first angle and half the second angle is 87 degrees. find the measure of the angles. What is the measure of the smaller angle?
what is the measure of the other?
Angle A + Angle B = 90º(complementary)
Therefore A = 90º - B
A + .5B = 87º
Substitute 90º - B for A in last equation to solve for B. Put that value in the first equation to find A. Check by putting both values in the last equation.
To find the measure of the angles, we can set up an equation using the given information.
Let's assume the first angle is represented by 'x' degrees, and the second angle is represented by 'y' degrees.
We are told that the two angles are complementary, which means the sum of their measures is 90 degrees. So, we can write the equation:
x + y = 90 (Equation 1)
We are also given that the sum of the measure of the first angle and half the second angle is 87 degrees. Since we know the measure of the first angle is 'x', and half the measure of the second angle is (y/2), we can write another equation:
x + (y/2) = 87 (Equation 2)
Now we have a system of two equations: Equation 1 and Equation 2.
To solve this system of equations, we can use the method of substitution. We'll solve Equation 1 for 'x' and substitute it into Equation 2.
From Equation 1, we get:
x = 90 - y
Substituting this value of 'x' into Equation 2, we have:
(90 - y) + (y/2) = 87
Simplifying the equation, we get:
90 - y + (y/2) = 87
To remove the fraction, we can multiply the entire equation by 2:
2(90 - y) + y = 2(87)
180 - 2y + y = 174
180 - y = 174
-y = 174 - 180
-y = -6
To isolate 'y', we multiply both sides by -1:
y = 6
Now substitute the value of 'y' back into either Equation 1 or Equation 2 to find the value of 'x'.
Using Equation 1:
x + y = 90
x + 6 = 90
x = 90 - 6
x = 84
So, the measure of the smaller angle is 84 degrees, and the measure of the other angle is 6 degrees.