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Sagot :

theleangreenbean

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!

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