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23 February, 05:58

If ef bisects angle ceb, angle cef=7x+31 and angle feb=10x-3

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  1. 23 February, 06:17
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    Given : Angle < CEB is bisected by EF.

    < CEF = 7x + 31.

    < FEB = 10x-3.

    We need to find the values of x and measure of < FEB, < CEF and < CEB.

    Solution: Angle < CEB is bisected into two angles < FEB and < CEF.

    Therefore, < FEB = < CEF.

    Substituting the values of < FEB and < CEF, we get

    10x - 3 = 7x + 31

    Adding 3 on both sides, we get

    10x - 3+3 = 7x + 31+3.

    10x = 7x + 34

    Subtracting 7x from both sides, we get

    10x-7x = 7x-7x + 34.

    3x = 34.

    Dividing both sides by 3, we get

    x = 11.33.

    Plugging value of x=11.33 in < CEF = 7x + 31.

    We get

    < CEF = 7 (11.33) + 31 = 79.33+31 = 110.33.

    < FEB = < CEF = 110.33 approximately

    < CEB = < FEB + < CEF = 110.33 + 110.33 = 220.66 approximately
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