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.

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