Question

Find the values of x and y.

Short answer

The value of x and y is 25 and 5 respectively.

Step-by-step solution

Step 1. Apply exterior angle theorem.

The measure of exterior angle of a triangle is the sum of measure of two remote interior angles of a triangle.

From the given diagram it can be observed that,

$$\begin{gathered} \left(x+2y\right)+90=125 \\ x+2y=125-90 \\ x+2y=35 \\ x=35-2y \end{gathered}$$

Step 2. Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is 180.

$$\begin{gathered} \left(x+2y\right)+90+\left(2x+y\right)=180 \\ 3x+3y=180-90 \\ 3x+3y=90 \\ x+y=30 \end{gathered}$$

Step 3. Description of step.

Substitute $35-2y$ for x into the equation obtained in Step 2 to find the value of y.

$$\begin{gathered} 35-2y+y=30 \\ -y=-5 \\ y=5 \end{gathered}$$

Step 4. Description of step.

Substitute 5 for y into the equation obtained in step 1 to find the value of x.

$\begin{array}{c}x=35-2\times 5\\ =35-10\end{array}$

$=25$

Therefore, the value of x and y is 25 and 5 respectively.