geometry question please help?

Segment BH bisects angle ABC, the measure of angle ABH=4x+7 and the measure of angle CBH=6x-3. Find the value of angle ABC.

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  • Anonymous
    1 decade ago
    Favorite Answer

    I made a picture so you can see how I got my answer.

    http://img90.imageshack.us/my.php?image=angleabcqn...

    Basically, you know that BH bisects angle ABC, so you just take the measures of angle ABH and CBH and set them equal to each other to solve for X.

    4x + 7 = 6x -3

    10 = 2x

    x = 5

    Now, add the two angles together and plug in two where X was.

    (4(5) + 7) + (6(5) -3) =

    (20 + 7) + (30 - 3) = 27 + 27

    = 54 degrees.

  • 1 decade ago

    Since angle ABH = angle CBH, 4x + 7 = 6x - 3

    4x + 7 = 6x - 3

    Subtract 4x from both sides

    7 = 2x - 3

    Add 3 to both sides

    10 = 2x

    Divide by 2 on both sides

    5 = x

    Add the 2 angles together to get angle ABC

    4x + 7 + 6x - 3 = 4(5) + 7 + 6(5) -3

    20 + 7 +30 -3

    54 degrees

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