Question

I need help with this problem I don’t understand it. The question is. Find the value of X___degreesY___degreesZ___degrees

Answer 1

SOLUTION

The fugure in the picture is a trapezoid.

Adjacent angles between the bases of a trapezoid are suplementary (add up to 180 degrees)

The bases of this trapezoid are the parallel sides PT and AR, so

$x\degree+y\degree=180\degree$

Now, since the trapezoid is an isosceles trapzoid, then the base angles will be equal, hence

$x=53\degree$

Hence x = 53 degrees

Then

$\begin{gathered} x+y=180\degree \\ 53+y=180\degree \\ y=180-53 \\ y=127\degree \end{gathered}$

hence y = 127 degrees

Also since it is an isosceles triangle the sides TR and AP would be equal

Hence z = 8