Chapter 4: Q8. (page 165)

Complete each sentence with the most appropriate word, phase or value.
8. In a quadrilateral EFGH, $\bar{EF} ∥ \bar{HG}$ , $m ∠ E = y + 10$ , $m ∠ F = 2 y - 40$ and $m ∠ H = 2 y - 31$ . $m ∠ G =$ ________ (numerical answer).

Short Answer

Expert verified

The answer is $m ∠ G = 86$ .

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, $m ∠ E = y + 10$ , $m ∠ F = 2 y - 40$ , $m ∠ H = 2 y - 31$ and .

Since, $E F ∥ H G$ in a quadrilateral, so,

$\begin{matrix} m ∠ E + m ∠ H = 180 \\ y + 10 + 2 y - 31 = 180 \\ 3 y - 21 = 180 \end{matrix}$

That implies,

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

…… [add 21 on each side]

That implies,

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

…… [ divide each side by 3]

That implies,

$y = 67$

Again,

$\begin{matrix} m ∠ F + m ∠ G = 180 \\ 2 y - 40 + m ∠ G = 180 \end{matrix}$

Putting y=67

$\begin{matrix} 2 (67) - 40 + m ∠ G = 180 \\ 94 + m ∠ G = 180 \end{matrix}$

That implies,

$m ∠ G = 180 - 94$

…… [Subtract 94 from each side]

Hence,

$m ∠ G = 86$

- State the conclusion.

Therefore,“In a quadrilateral EFGH, $E F ∥ H G$ , $m ∠ E = y + 10$ , $m ∠ F = 2 y - 40$ and $m ∠ H = 2 y - 31$ . $m ∠ G =$ 86.”

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Complete each sentence with the most appropriate word, phase or value.
8. In a quadrilateral EFGH, $\bar{EF} ∥ \bar{HG}$ , $m ∠ E = y + 10$ , $m ∠ F = 2 y - 40$ and $m ∠ H = 2 y - 31$ . $m ∠ G =$ ________ (numerical answer).

Short Answer

Step by step solution

- State the definition of a quadrilateral.

- Show the calculation.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Mechanics Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Complete each sentence with the most appropriate word, phase or value.8. In a quadrilateral EFGH, EF¯∥HG¯,m∠E=y+10, m∠F=2y−40 andm∠H=2y−31 .m∠G= ________ (numerical answer).

Short Answer

Step by step solution

- State the definition of a quadrilateral.

- Show the calculation.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Mechanics Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Complete each sentence with the most appropriate word, phase or value.
8. In a quadrilateral EFGH, $\bar{EF} ∥ \bar{HG}$ , $m ∠ E = y + 10$ , $m ∠ F = 2 y - 40$ and $m ∠ H = 2 y - 31$ . $m ∠ G =$ ________ (numerical answer).