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Chapter 4: Q8. (page 165)

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

8. In a quadrilateral EFGH, EF炉鈭�HG炉,m鈭�E=y+10, m鈭�F=2y鈭�40 andm鈭�H=2y鈭�31 .m鈭�G= ________ (numerical answer).

Short Answer

Expert verified

The answer is m鈭�G=86.

Step by step solution

01

- State the definition of a quadrilateral. 

A quadrilateral is a polygon that has exactly 4 sides.

02

- Show the calculation.

Given that: In a quadrilateral EFGH, m鈭�E=y+10,m鈭�F=2y鈭�40 , m鈭�H=2y鈭�31 and .

Since,EF鈭�HG in a quadrilateral, so,

m鈭�E+m鈭�H=180y+10+2y鈭�31=1803y鈭�21=180

That implies,

role="math" 3y=180+21

鈥︹�� [add 21 on each side]

That implies,

y=2013

鈥︹�� [ divide each side by 3]

That implies,

y=67

Again,

m鈭�F+m鈭�G=1802y鈭�40+m鈭�G=180

Putting y=67

2(67)鈭�40+m鈭�G=18094+m鈭�G=180

That implies,

m鈭�G=180鈭�94

鈥︹�� [Subtract 94 from each side]

Hence,

m鈭�G=86

03

- State the conclusion.

Therefore,鈥淚n a quadrilateral EFGH,EF鈭�HG,m鈭�E=y+10 , m鈭�F=2y鈭�40 andm鈭�H=2y鈭�31 .m鈭�G= 86.鈥�

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