Answer:
x = 25; both labeled angles are 65º
Explanation:
To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.
In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.
Thus,
(3x - 10)° = (x + 40)°
Solve for x
3x - 10 = x + 40
Subtract x from both sides
3x - 10 - x = x + 40 - x
3x - x - 10 = x - x + 40
2x - 10 = 40
Add 10 to both sides
2x - 10 + 10 = 40 + 10
2x = 50
Divide both sides by 2
2x/2 = 50/2
x = 25
*Plug in the value of x to find the measure of each labelled angles:
(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°
(x + 40)° = 25 + 40 = 65°