Question

Consider isosceles trapezoid TRAP above. What is the value of y?

Answer 1

well, TP = RA, the heck does that mean? well, besides making the trapezoid an isosceles one, it means that ∡T = ∡R and ∡P = ∡A.

Now, the sum of all interior angles in a polygon is 180(n - 2), n = sides, this one has four sides so it has a total sum of interior angles of 180(4 - 2) = 360°.

`4(3y+2)+4(3y+2)+64+64=360 \\\\\\ 12y+8+12y+8+64+64=360\implies 24y+144=360\implies 24y=216 \\\\\\ y=\cfrac{216}{24}\implies y=9`