Question

In Exercises 37– 40, BD ⃗ bisects ∠ABC. Find m∠ABD,

m∠CBD, and m∠ABC.

Answer 1

37, ABD = CBD = 44 degrees, and ABC = 88 degrees

38. ABD = CBD = 24 degrees, and ABC = 48 degrees

39. ABD = CBD = 65 degrees, and ABC = 130 degrees

40. ABD = CBD =67 degrees, and ABC = 134 degrees

Explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees