y = 32, x = 43
To figure this out, you have to use what you know to find all sorts of measures.
Lets start with the 75 degree angle. We know that the opposite side is a vertical angle, so that is also equal to 75 degrees. Since the angle to the big triangle is a supplementary angle, we know that the sum of 75 degrees and that angle is 180 degrees. Do the math and we get 180 - 75, or 105 degrees. The angles of a triangle always add up to 180, so 105 + 43 + y = 180. Solve for y: [tex]148+y=180=148-148+y=180-148=y=32[/tex]. So y is equal to 32 degrees. Now to find x, we know that the bases of the triangles are parallel, and that there is a line that goes straight from angle y to one of our unknown angles. Because the triangle bases are parallel and the y to unknown line does not change, we can tell that those are the same. So y = unknown angle 1, or 32 = 32. So, we know the measure of one angle. The other unknown angle is vertical to the other angle we found earlier, 105. So, we get 105 + 32 + x = 180. Evaluate: [tex]32+105+x=180=137+x=180=137-137+x=180-137=x=43[/tex]. So x is equal to 43.
