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# ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral. Q.8

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How i find the angles of this question. This is very important question of class 10th So please help me solving this question. ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.

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1. It is known thatÂ the sum of the opposite angles of a cyclic quadrilateral is 180o

Thus, we have

âˆ C +âˆ A = 180

4y + 20âˆ’ 4x = 180

âˆ’ 4x + 4y = 160

x âˆ’ y = âˆ’ 40 â€¦â€¦â€¦â€¦â€¦(1)

And, âˆ B + âˆ D = 180

3y âˆ’ 5 âˆ’ 7x + 5 = 180

âˆ’ 7x + 3y = 180 â€¦â€¦â€¦..(2)

Multiplying 3 to equation (1), we get

3x âˆ’ 3y = âˆ’ 120 â€¦â€¦â€¦(3)

Adding equation (2) to equation (3), we get

âˆ’ 7x + 3x = 180 â€“ 120

âˆ’ 4x = 60

x = âˆ’15

Substituting this value in equation (i), we get

x âˆ’ y = âˆ’ 40

-yâˆ’15 = âˆ’ 40

y = 40-15

= 25

âˆ A = 4y + 20 = 20+4(25) = 120Â°

âˆ B = 3y âˆ’ 5 = âˆ’ 5+3(25)Â = 70Â°

âˆ C = âˆ’ 4x = âˆ’ 4(âˆ’ 15) = 60Â°

âˆ D =Â 5-7x

âˆ D=Â 5âˆ’ 7(âˆ’15) = 110Â°

Hence, all the angles are measured.

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