Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 87.75 degrees. Find the measures of the angles? What is the measure of the smaller angle? What is the measure of the other angle. Both in degrees...
a + b = 90
a + .25 b = 87.75
so b = 90-a
a + .25(90-a) = 87.75
.75 a + 22.50 = 87.75
etc
I am very confused?
The measure of an angle is 48°. What is the measure of a complementary angle?
To solve this problem, let's first establish the variables for the two angles. Let's call the first angle x and the second angle y.
Given that the two angles are complementary, we know that the sum of their measures is 90 degrees. So, we can write the equation:
x + y = 90 (Equation 1)
The problem also states that the sum of the measure of the first angle and one-fourth the second angle is 87.75 degrees. Therefore, we can write another equation:
x + (1/4)y = 87.75 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and y). To solve this system, we can use the method of substitution.
First, we can solve Equation 2 for x in terms of y:
x = 87.75 - (1/4)y
Next, we substitute this expression for x into Equation 1:
(87.75 - (1/4)y) + y = 90
To simplify, we can combine like terms:
87.75 - (1/4)y + y = 90
87.75 + (3/4)y = 90
Next, we can isolate the y term by subtracting 87.75 from both sides:
(3/4)y = 90 - 87.75
(3/4)y = 2.25
To solve for y, we divide both sides of the equation by (3/4):
y = (2.25) / (3/4)
y = 2.25 * (4/3)
y = 3
So, the second angle is y = 3 degrees.
To find the measure of the first angle, we can substitute the value of y into Equation 1:
x + 3 = 90
Subtracting 3 from both sides:
x = 90 - 3
x = 87
Therefore, the first angle is x = 87 degrees.
To determine which angle is smaller, we compare the values of x and y. Since x = 87 degrees and y = 3 degrees, we can conclude that the smaller angle is y, which measures 3 degrees. The other angle, which measures 87 degrees, is larger.