Find mZABD and mZCBD given m ABC = 111º. A
(-10x + 58)
D
(6x + 41)
B
С
17

m∠CBD=98 °

Step-by-step explanation:

m\angle ABDm∠ABD is a straight angle.

m\angle ABC=2x+50m∠ABC=2x+50 °

m\angle CBD=6x+2m∠CBD=6x+2 °

∵ m\angle ABDm∠ABD is a straight angle.

∴ m\angle ABDm∠ABD is equal to 180°.

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

\begin{gathered}\angle ABD=\angle ABC+\angle CBD\\180=2x+50+6x+2\\180=8x+52\\8x=180-52\\8x=128\\x=\frac{128}{8}=16\end{gathered}∠ABD=∠ABC+∠CBD180=2x+50+6x+2180=8x+528x=180−528x=128x=8128=16

∴ x=16.

Now, m\angle CBD=6x+2m∠CBD=6x+2

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

m\angle CBD=6x+2=6(16)+2=96+2=98m∠CBD=6x+2=6(16)+2=96+2=98 °.

Therefore, m\angle CBD=98m∠CBD=98 °.

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step-by-step explanation: