two angles are complimentary. The sum of the measure of the first angle and half the second angle is 75 degrees. Find the measure of the angles.
What is the measure of the smaller angle?
what is the measure of the other angle?
x + y = 90
x + .5y = 75
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.5 y = 15
y = 30 etc
In any triangle, the sum of the measures of the angles is 180degrees. In triangle ABC, angle A is four times as large as angle B. Angle C measures 20degrees less than angle B. Find the measure of each angle.
To find the measures of the angles, let's set up an equation based on the given information.
Let's denote the measure of the first angle as x and the measure of the second angle as y.
The first piece of information states that the two angles are complementary, which means they add up to 90 degrees. So, we have the equation:
x + y = 90 (Equation 1)
The second piece of information states that the sum of the measure of the first angle (x) and half the measure of the second angle (0.5y) is 75 degrees. So, we have another equation:
x + 0.5y = 75 (Equation 2)
Now we have a system of two equations. We can solve this system using substitution or elimination.
Let's solve it using elimination:
Multiply Equation 2 by 2 to make the coefficients of y the same in both equations:
2(x + 0.5y) = 2(75)
2x + y = 150 (Equation 3)
Now we can subtract Equation 1 from Equation 3:
(2x + y) - (x + y) = 150 - 90
x = 60
Substitute the value of x into Equation 1 to find y:
60 + y = 90
y = 90 - 60
y = 30
Therefore, the measure of the smaller angle (x) is 60 degrees, and the measure of the other angle (y) is 30 degrees.