Pls help I don't understand this

m∠ABD = 67°

m∠CBD = 67°

m∠ABC = 134°

Step-by-step explanation:

The definition of an angle bisector means that it splits an angle into two equal measures.

So (8x + 35) = (11x + 23)

8x + 35 = 11x + 23

-8x         - 8x

35 = 3x + 23

-23         - 23

12 = 3x

12 / 3 = 3x / 3

4 = x

Now, we input x back into the equations and solve, to make sure we have solved for x correctly.

8(4) + 35 = 11(4) + 23

32 + 35 = 44 + 23

67 = 67

So, m∠ABD = 67°, m∠CBD = 67°, and m∠ABC = (67 + 67 = ) 134°

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

-3 degrees

step-by-step explanation: