Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 35 Page 132

m∠ AEC=74

Practice makes perfect

To find the value of m∠ AEC, we first need to find the value of y. To do so, we recognize that the labeled angles are vertical angles. Therefore, they are congruent by the Vertical Angles Theorem.

This means we can equate the expressions for the two angle measures and solve for y.
3y+20=5y-16
Solve for y
3y+36=5y
36=2y
18=y
y=18
Now that we know the y-variable, we can substitute the value into the expression for m∠ AEC to find its value.
3y+20
3( 18)+20
54+20
74
We have found that m∠ AEC=74.