Question

How do I correctly solve this?

Answer 1

Answer:   14

Step-by-step explanation:

Since BD is parallel to EG, then ∠BCF and ∠EFC are consecutive (same side interior) angles, which means they are supplementary angles.  

∠BCF + ∠EFC = 180

(5x - 66) + (2x + 50) = 180

7x - 16 = 180

7x        = 196

 x        = 28

∠BCF ≅ ∠EFC because they are vertical angles.

∠BCF = ∠EFC

5(28) - 66 = 9y - 52

140 - 66 + 52 = 9y

192 = 9y

14 = y

Answer 2

Answer: y = 14

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Explanation:

The two angles involving x add up to 180 degrees. This is because they are same side interior angles (and because the horizontal lines are parallel)

So,

(angle BCF) + (angle EFC) = 180

(5x - 66) + (2x + 50) = 180

5x - 66 + 2x + 50 = 180

7x - 16 = 180

7x - 16+16 = 180+16 ... add 16 to both sides

7x = 196

7x/7 = 196/7 .... divide both sides by 7

x = 28

This will be used to help find y

Notice how the angles BCF and ACD are vertical angles, therefore they are congruent or the same measure

angle ACD = angle BCF

9y - 52 = 5x - 66

9y - 52 = 5*28 - 66 ..... replace x with 28 (since x = 28)

9y - 52 = 140 - 66

9y - 52 = 74

9y - 52+52 = 74+52 .... add 52 to both sides

9y = 126

9y/9 = 126/9 .... divide both sides by 9

y = 14