The difference between the measures of two supplementary angles is 8˚. What is the measure of the larger angle?
What is the measure of the smaller angle?
x -(180-x) = 8
2 x -180 = 8
2 x = 188
x = 94
180 - x = 86
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Let's denote the measure of the larger angle as x degrees and the measure of the smaller angle as y degrees.
Since two angles are supplementary, their sum is always 180 degrees.
According to the given information, the difference between the measures of the two supplementary angles is 8 degrees. This can be represented as:
x - y = 8 (Equation 1)
We also know that the sum of the two angles is 180 degrees:
x + y = 180 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the method of substitution. We can rearrange Equation 1 to solve for x:
x = y + 8
Substitute this expression for x into Equation 2:
(y + 8) + y = 180
Combine like terms:
2y + 8 = 180
Subtract 8 from both sides:
2y = 172
Divide both sides by 2:
y = 86
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x - 86 = 8
Add 86 to both sides:
x = 94
Therefore, the measure of the larger angle is 94 degrees, and the measure of the smaller angle is 86 degrees.
To find the measures of the two supplementary angles, let's first assign variables to represent the angles.
Let's assume the larger angle to be x degrees. Therefore, the smaller angle would be (x - 8) degrees because it is given that the difference between the two angles is 8 degrees.
Now, we know that supplementary angles add up to 180 degrees. So, we can set up the following equation:
x + (x - 8) = 180
Combining like terms on the left side of the equation:
2x - 8 = 180
Adding 8 to both sides of the equation:
2x = 188
Dividing both sides by 2:
x = 94
Therefore, the measure of the larger angle is 94 degrees, and the measure of the smaller angle is (94 - 8) = 86 degrees.