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28 April, 23:58

If the measure of angle ABF=6x+26 and the measure of angle EBF=2x9 and measure of angle ABE = 11x-31 find the measure of angle ABF

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  1. 29 April, 00:13
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    Its not clearly given that whether EBF = 2x + 9 or 2x - 9.

    I have written the solution for both.

    If EBF = 2x + 9,

    then ABF = 6x + 26 and ABE = 11x - 31.

    Now, ABE = ABF + EBF

    11x - 31 = (6x + 26) + (2x + 9)

    = (6x + 2x) + (26 + 9)

    = 8x + 35

    11x - 8x = 35 + 31

    3x = 66

    x = 22

    Therefore, ABF = 6x + 26 = 6 (22) + 26 = 132 + 26 = 158°

    If EBF = 2x - 9,

    then ABF = 6x + 26 and ABE = 11x - 31.

    Now, ABE = ABF + EBF

    11x - 31 = (6x + 26) + (2x - 9)

    = (6x + 2x) + (26 - 9)

    = 8x + 17

    11x - 8x = 17 + 31

    3x = 48

    x = 16

    Therefore, ABF = 6x + 26 = 6 (16) + 26 = 96 + 26 = 122°
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