the measure of one angle is 2/3 the measure of the other totaling 180
(2/3) x + x = 180
(5/3) x = 180
x = 108
(2/3) x = 72
To find the measures of the angles, we can define one angle as x degrees. Since the measure of one angle is 2/3 the measure of the other, the second angle can be represented as (2/3)x degrees.
According to the problem, the total of these two angles is 180 degrees. So, we can set up an equation:
x + (2/3)x = 180
To solve the equation, we need to remove the fraction. We can do this by multiplying the entire equation by the denominator of the fraction, which is 3:
3(x) + 3((2/3)x) = 3(180)
3x + 2x = 540
5x = 540
Dividing both sides of the equation by 5:
x = 540/5
x = 108
Therefore, one angle measures 108 degrees.
To find the other angle, substitute the value of x back into the equation for the second angle:
(2/3)x = (2/3)(108) = 72
The other angle measures 72 degrees.