Question

find the values of X and Y in the image below and then find the measures of the four angles in the trapezoid

Answer 1

Answer:

x = 45, y = 115; 90, 90, 115, 65

Explanation:

One of the properties of a trapezoid is that adjacent angles of the legs of the trapezoid are supplementary, that is, they add up to 180 degrees.

Considering the above property, we'll have;

$\begin{gathered} y+(y-50)=180 \\ 2y-50=180 \\ 2y=180+50 \\ y=\frac{130}{2} \\ y=115^{\circ} \end{gathered}$

Still considering the above property, we have;

$\begin{gathered} 2x+90=180 \\ 2x=180-90 \\ x=\frac{90}{2} \\ x=45 \end{gathered}$

We can see that the measure of the four angles of the trapezoid are;

$\begin{gathered} 2x=2(45)=90^{\circ} \\ \text{Right angle = 90}^{\circ} \\ y=115^{\circ} \\ (y-50)=115-50=65^{\circ} \end{gathered}$