Question

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

Answer 1

Answer:

$m\angle CBD=98$°

Step-by-step 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,

$\angle ABD=\angle ABC+\angle CBD\\180=2x+50+6x+2\\180=8x+52\\8x=180-52\\8x=128\\x=\frac{128}{8}=16$

∴ 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, $m\angle CBD=98$°.