What are the values of x and y in this figure? a. x=55,y=125 b. x=110,y=70 c. x=110,y=35 d. x=55,y=62.5

Hello!

We know that the sum of all angles in a triangle is 180 degrees. This can be represented by the following formula:

(angle 1) + (angle 2) + (angle 3) = 180

Insert all known values and variables of triangle ABC into the formula above:

30 + (80 + y) + y = 180

Simplify and combine like terms:

30 + 80 + y + y = 180
110 + 2y = 180

Now subtract 110 from both sides of the equation:

2y = 70

Divide both sides by 2:

y = 35

We have now proven that Y is equal to 35 degrees. Using the known value of Y, we can find the value of X using the same formula as above. Begin by inserting all known values and variables of triangle BCD:

y + y + x = 180
(35) + (35) + x = 180

Combine like terms:

70 + x = 180

Subtract 70 from both sides of the equation:

x = 110

We have now proven that X is equal to 110 degrees. Therefore, considering the known values of X and Y, the answer to this problem is C.

I hope this helps!