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# 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.

### 2 Answers

- Anonymous1 decade agoFavorite 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