Question

Directions attatched

Answer 1

Answer:

• x=7
• ∠GBD=112
• ∠EFC=112

Step-by-step explanation:

Here, we need to know about the concept of the alternate interior angle theorem. This says that the alternate interior angle of two parallel lines formed with one transversal is equal. For a more graphical explanation, please refer to the attachment below.

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Given

∠GBD=4x+84

∠EFC=16x

m∠GBD=m∠EFC

Solve

4x+84=16x ⇔ Given

4x+84-4x=16x-4x ⇔ Subtract 4x on both sides

84=12x ⇔ Simplify

84/12=12x/12 ⇔ Divide 12 on both sides

x=7 ⇔ Simplify

Substitute the x value into each angle expression

∠GBD=4x+84=4(7)+84=28+84=112

∠EFC=16x=16(7)=112

Hope this helps!! :)

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