the measures of 2 supplementary angles have the ratio 2is to 3.find the measureof each angle?
3x + 2x = 180º
Solve for x, then 3x and 2x.
36
Supplementary angles are angles whose sum is 180°. Two supplementary angles are such that one angle is
3
3
degrees
°
less than
less than
twice
twice the other. Find the measures of the angles.
To find the measure of each angle, we first need to understand what it means for two angles to be supplementary. Supplementary angles are two angles that add up to 180 degrees.
Let's assume that the two angles have measures of 2x and 3x, where x is a common factor.
According to the problem, the ratio of the measures of the two angles is 2:3. This means that the measure of the first angle is 2 times some factor, and the measure of the second angle is 3 times that same factor.
So, we have the equation:
2x + 3x = 180
Combining like terms, we get:
5x = 180
To solve for x, we divide both sides of the equation by 5:
x = 180/5
x = 36
Now that we know the value of x, we can substitute it back into the expressions for the measures of the angles:
First angle = 2x = 2 * 36 = 72 degrees
Second angle = 3x = 3 * 36 = 108 degrees
Therefore, the measure of the first angle is 72 degrees, and the measure of the second angle is 108 degrees.