Question

Two angles are supplementary. their difference is 106 degrees. find the larger angle____

Answer 1

To find the larger of two supplementary angles whose difference is 106 degrees, equations can be set up and solved to find that the larger angle is 143 degrees.

Step-by-step explanation:

When two angles are supplementary, their sum is 180 degrees. If their difference is 106 degrees, we can set up two equations to find the larger angle.

1. Let the larger angle be x and the smaller angle be y.
2. The sum of the angles: x + y = 180 degrees.
3. The difference of the angles: x - y = 106 degrees.
4. We can now add these two equations.

x + y + (x - y) = 180 degrees + 106 degrees

2x = 286 degrees

x = 286 degrees / 2

x = 143 degrees

Therefore, the larger angle is 143 degrees.