- For question 1-
Given line a and line b are parallel lines, the angle represented with 15x and angle angle represented with 6x + 54 are alternate. Therefore, they are congruent, so we can write the following equation:
15x = 6x + 54
- Transfer like terms to the same side of the equation.
15x - 6x = 54
9x = 54
x = 6
So the measure of the angle represented with 15x is equal to 90°.
- For question 2-
The angle with a measure of 105° and the angle represented with 5y are alternate angles and congruent.
So,
5y = 105
- Divide both sides by 5 to isolate y.
y = 21