Question

Given

mZABD is a straight angle.
m
ABC = 2x + 50°
mZCBD = 6x + 2°
Find mZCBD:

Answer 1

`m\angle CBD=98`°

Explanation:

Given:

`m\angle ABD` is a straight angle.

`m\angle ABC=2x+50`°

`m\angle CBD=6x+2`°

∵
`m\angle ABD` is a straight angle.

∴
`m\angle ABD` is equal to 180°.

Now, angle ABD is a sum of angles ABC and CBD. This gives,

`\angle ABD=\angle ABC+\angle CBD\\180=2x+50+6x+2\\180=8x+52\\8x=180-52\\8x=128\\x=(128)/(8)=16`

∴ x=16.

Now,
`m\angle CBD=6x+2`

Plug in 16 for
`x` and calculate angle CBD. This gives,

`m\angle CBD=6x+2=6(16)+2=96+2=98`°.

Therefore,
`m\angle CBD=98`°.