Question

Complete each sentence with the most appropriate word, phase or value.

8. In a quadrilateral EFGH, $\overline{\text{EF}}\parallel \overline{\text{HG}}$,$\text{m}\angle \text{E}=\text{y}+\mathbf{10}$, $\text{m}\angle \text{F}=\mathbf{2}\text{y}-\mathbf{40}$ and$\text{m}\angle \text{H}=\mathbf{2}\text{y}-\mathbf{31}$ .$\text{m}\angle \text{G}=$ ________ (numerical answer).

Short answer

The answer is $\text{m}\angle \text{G}=\mathbf{86}$.

Step-by-step solution

- State the definition of a quadrilateral. 

A quadrilateral is a polygon that has exactly 4 sides.

- Show the calculation.

Given that: In a quadrilateral EFGH, $m\angle E=y+10$,$m\angle F=2y-40$ , $m\angle H=2y-31$ and .

Since,$EF\parallel HG$ in a quadrilateral, so,

$\begin{array}{c}m\angle E+m\angle H=180\\ y+10+2y-31=180\\ 3y-21=180\end{array}$

That implies,

role="math" $3y=180+21$

…… [add 21 on each side]

That implies,

$y=\frac{201}{3}$

…… [ divide each side by 3]

That implies,

$y=67$

Again,

$\begin{array}{c}m\angle F+m\angle G=180\\ 2y-40+m\angle G=180\end{array}$

Putting y=67

$\begin{array}{c}2\left(67\right)-40+m\angle G=180\\ 94+m\angle G=180\end{array}$

That implies,

$m\angle G=180-94$

…… [Subtract 94 from each side]

Hence,

$m\angle G=86$

- State the conclusion.

Therefore,“In a quadrilateral EFGH,$EF\parallel HG$,$m\angle E=y+10$ , $m\angle F=2y-40$ and$m\angle H=2y-31$ .$m\angle G=$ 86.”