Answer:
106 degrees
Step-by-step explanation:
Sides AB and CD are equal in length and sides AD and BC are parallel to each other. This tells us that angles B and C are equivalent. Knowing this, we can set up the following equation to solve for x:
[tex]4x+42=74+2x[/tex]
Subtract both sides by 42
[tex]4x+42-42=74+2x-42\\4x=32+2x[/tex]
Subtract both sides by 2x
[tex]4x-2x=32+2x-2x\\2x=32[/tex]
Divide both sides by 2
[tex]\frac{2x}{2} =\frac{32}{2} \\x=16[/tex]
Now, to find angle ABC, or angle B, we can plug x back into its expression:
[tex]4x+42\\= 4(16)+42\\=64+42\\= 106[/tex]
Therefore, the measure of angle ABC is 106 degrees.
I hope this helps!
