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

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

Step-by-step 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=(130)/(2) \\ y=115^(\circ) \end{gathered}`

Still considering the above property, we have;

`\begin{gathered} 2x+90=180 \\ 2x=180-90 \\ x=(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}`