Answer:
[tex]m\angle CBD=98[/tex]°
Step-by-step explanation:
Given:
[tex]m\angle ABD[/tex] is a straight angle.
[tex]m\angle ABC=2x+50[/tex]°
[tex]m\angle CBD=6x+2[/tex]°
∵ [tex]m\angle ABD[/tex] is a straight angle.
∴ [tex]m\angle ABD[/tex] is equal to 180°.
Now, angle ABD is a sum of angles ABC and CBD. This gives,
[tex]\angle ABD=\angle ABC+\angle CBD\\180=2x+50+6x+2\\180=8x+52\\8x=180-52\\8x=128\\x=\frac{128}{8}=16[/tex]
∴ x=16.
Now, [tex]m\angle CBD=6x+2[/tex]
Plug in 16 for [tex]x[/tex] and calculate angle CBD. This gives,
[tex]m\angle CBD=6x+2=6(16)+2=96+2=98[/tex]°.
Therefore, [tex]m\angle CBD=98[/tex]°.
