Question

If measure of ∠p is three less than twice the measure of ∠q, and ∠p and ∠q are supplementary angles, find each angle measure?

Answer 1

the measure of ∠p is 119 degrees, and the measure of ∠q is 61 degrees.

Explanation:

Let's denote the measure of ∠p as "x" and the measure of ∠q as "y".

According to the given information:

1) The measure of ∠p is three less than twice the measure of ∠q:

x = 2y - 3

2) ∠p and ∠q are supplementary angles:

x + y = 180

We can now solve the system of equations to find the values of x and y.

Substituting the value of x from equation 1 into equation 2, we get:

(2y - 3) + y = 180

3y - 3 = 180

3y = 183

y = 61

Now, substituting the value of y back into equation 1, we can find x:

x = 2(61) - 3

x = 122 - 3

x = 119