Question

In two supplementary angles, the measure of one angle is 6

more than twice the measure of the other. The measures of
these two angles are
A) 26° and 62°
B) 32° and 58°
C) 58° and 122°
D) 62° and 118°

Answer 1

To find the measures of the angles, set up and solve a system of equations. The measures are 58° and 122°.

Step-by-step explanation:

To solve this problem, let's represent the measures of the two angles as x and y. We are given that the measure of one angle is 6 more than twice the measure of the other, so we can write the equation x = 2y + 6. Additionally, we know that the two angles are supplementary, which means their measures add up to 180 degrees. We can write the equation x + y = 180.

Now we have a system of two equations:

x = 2y + 6

x + y = 180

We can solve this system of equations to find the measures of the two angles. By substituting the value of x from the first equation into the second equation, we get (2y + 6) + y = 180. Simplifying this equation gives us 3y + 6 = 180. Solving for y, we subtract 6 from both sides to get 3y = 174. Dividing both sides by 3, we find y = 58. Substituting this value back into the first equation, we find x = 2(58) + 6 = 122.

Therefore, the measures of the two angles are 58° and 122°. So, the correct option is (C) 58° and 122°.