Question

Just tell me how to set up the equation.

Answer 1

Explanation:

• Find angle CBD

CBD+D+C=180

CBD+83+22x=180

• ABD will be 180-angle CBD

180-CBD= 50x-1 (ABD)

CBD=180-50x+1

• Solve this to find angle B

¹ CBD=180-50x+1

CBD+83+22x=180 ⇒ CBD=180-83-22x ⇒²CBD=97-22x

Equate ¹ and²

180-50x+1=97-22x

-28x=-84

x=3

22x=22×3=66

180-(66+83)=31=angle B for CBD

so you can find ABD ( use 180-31= 50x-1; solve for x; x should be 3)

substitute your value of x in 50x-1

(so ABD=149; 149+31=180 so you know you're right)

Answer 2

ABD = 149

Explanation:

The exterior angle of a triangle is the sum of the opposite interior angles

50x -1 = 22x+83

Subtract 22x from each side

50x-22x-1 = 22x-22x+83

28x -1 = 83

Add 1 to each side

28x-1+1 = 83+1

28x =84

Divide by 28

28x/28x = 84/28

x = 3

Now we want to find ABD

ABD = 50x-1

=50(3)-1

150-1

149