Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measure of the angle's supplement.
The measure of the angle is four times greater than its supplement.
What is the measure of the supplement?
supplementary angles sum to 180º
angle + supplement = 180º
Let x represent the degree measure of the angle's supplement.
If the measure of the angle is four times greater than its supplement, we can set up the equation:
angle measure = 4 * supplement measure
Since the measure of the angle is four times greater than its supplement, we have:
angle measure = x + 4x
Simplifying the equation:
angle measure = 5x
Since we know that the measure of the angle is equal to 5x, and we want to find the measure of the supplement, we can set up the equation:
5x = supplement measure
To solve for x, divide both sides of the equation by 5:
x = supplement measure / 5
Therefore, the measure of the supplement is x/5.
To solve this problem using an algebraic equation, we can start by representing the measure of the angle's supplement as x. According to the given information, the measure of the angle is four times greater than its supplement.
Therefore, we can express the measure of the angle as 4x. Recall that the sum of an angle and its supplement is always 180 degrees since they are supplementary angles.
So, we can set up the equation:
x + 4x = 180
Now, we can simplify and solve for x:
5x = 180
x = 180/5
x = 36
Therefore, the measure of the supplement is 36 degrees since we let x represent its degree measure.