Question

Find the values of x and y.

In equilateral$\mathrm{\Delta }\mathit{D}\mathit{E}\mathit{F}\mathbf{,}$$\mathit{m}\angle \mathit{D}\mathbf{=}\mathit{x}\mathbf{+}\mathit{y}$ and $\mathit{m}\angle \mathit{E}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{-}\mathit{y}$.

Short answer

The value of$x$ and$y$ is 40and 20 respectively.

Step-by-step solution

Step 1. Apply definition of equilateral triangle.

An equilateral triangle is a triangle which all the three angles are equal in length, that is, $60°$.

Therefore, in $\mathrm{\Delta }DEF$, $m\angle D=m\angle E=m\angle F=60$.

Step 2. Description of step.

Consider, $m\angle D=60$.

Substitute $x+y$for $m\angle D$into $m\angle D=60$and simplify.

$x+y=60$

Step 3. Description of step.

Consider, $m\angle E=60$.

Substitute $2x-y$for $m\angle E$into $m\angle E=60$and simplify.

$2x-y=60$

Step 4. Description of step.

Add $x+y=60$and $2x-y=60$, to find the value of $x$.

$$\begin{gathered} x+y+2x-y=60+60 \\ 3x=120 \\ x=40 \end{gathered}$$

Step 5. Description of step.

Substitute 40 for$x$ into $x+y=60$, to find the value of $y$.

$$\begin{gathered} 40+y=60 \\ y=60-40 \\ =20 \end{gathered}$$

Therefore, the value of$x$ and$y$is 40 and 20 respectively.