Question

Find x and y. use proper postulates or theorems to justify your answer

Answer 1

x = 110 & y = 28

Explanation:

The top and bottom lines are both intersected by a transversal. Because of this, we can say the 100-degree angle is equivalent to the (x-10) angle due to the Corresponding Angles Theorem.

If 100 = x -10 then you add 10 to both sides to get x = 110 degrees.

Then, using the Same Side Exterior Angles Postulate, you can conclude that the 100-angle and the (2y + 24) angle are supplementary, meaning they add up to 180 degrees.

So, 100 + (2y + 24) = 180.

Subtract 100 from both sides to get 2y + 24 = 80

Then subtract 24 from both sides to get 2y = 56

And divide both sides by 2 to get y = 28 degrees.