Question

(40 points best answer) (asap!)

In the image below, (AD) ̅ is an angle bisector, (AB) ̅=42, (AC) ̅=35, and (BC) ̅=44. Find the measure of m.

Answer 1

24 =m

Explanation:

We can use the angle bisector theorem

AB AC

--------- = ----------

BD DC

Substituting in known values

42 35

------ = -----------

m n

BC = 44 We know that 44 = m+n. Solving for n n = 44-m

42 35

------ = -----------

m 44-m

Using cross products

42(44-m) = 35m

Distribute

1848 -42m = 35m

Add 42m to each side

1848 -42m+42m = 35m+42m

1848 = 77m

Divide each side by 77

1848/77 = 77m/77

24 =m