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AnilSinghBora
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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 that the sum of the opposite angles of a cyclic quadrilateral is 180o

    Thus, we have

    ∠C +∠A = 180

    4y + 20− 4x = 180

    − 4x + 4y = 160

    x − y = − 40 ……………(1)

    And, ∠B + ∠D = 180

    3y − 5 − 7x + 5 = 180

    − 7x + 3y = 180 ………..(2)

    Multiplying 3 to equation (1), we get

    3x − 3y = − 120 ………(3)

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

    − 7x + 3x = 180 – 120

    − 4x = 60

    x = −15

    Substituting this value in equation (i), we get

    x − y = − 40

    -y−15 = − 40

    y = 40-15

    = 25

    ∠A = 4y + 20 = 20+4(25) = 120°

    ∠B = 3y − 5 = − 5+3(25) = 70°

    ∠C = − 4x = − 4(− 15) = 60°

    ∠D = 5-7x

    ∠D= 5− 7(−15) = 110°

    Hence, all the angles are measured.

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