he sum of the measure of the two vertical angles is 10 times the measuresof the supplement of oneof the angle find the measure of one of the vertical angles

To solve this problem, we can use the information given about vertical angles and supplements.

Let's assume one of the vertical angles has a measure of x degrees. Since vertical angles are congruent, the other vertical angle will also have a measure of x degrees.

The supplement of an angle is the angle that, when added to the original angle, gives a sum of 180 degrees.

So, the supplement of one of the vertical angles would have a measure of 180 - x degrees.

According to the given information, the sum of the measure of the two vertical angles is 10 times the measure of the supplement of one of the angles:

x + x = 10 * (180 - x)

Simplifying this equation, we get:

2x = 10 * (180 - x)

Distributing the 10 on the right side, we have:

2x = 1800 - 10x

Combining like terms, we get:

2x + 10x = 1800

12x = 1800

Dividing both sides by 12, we find:

x = 150

Therefore, one of the vertical angles has a measure of 150 degrees.