McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Rectangles
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Exercise 12 Page 508

Recall that diagonals in a rectangle are congruent and bisect each other.

50

Practice makes perfect
We are asked to find the measure of ∠CEB using the given information. Let's notice that, since diagonals in a rectangle are congruent and bisect each other, AE=DE. This means that triangle AED is an isosceles triangle and m∠DAE=m∠ ADE.
Using the Triangle Sum Theorem, we can find the measure of ∠DEA. Let's recall that according to this theorem the sum of the measures of angles in a triangle is always 180. We will use the fact we found above that m∠DAE=m∠ADE.
m∠DAE+m∠ADE+m∠DEA=180
m∠DAE+ m∠DAE+m∠DEA=180
65+ 65+m∠DEA=180
130+m∠DEA=180
m∠DEA=50
We found that the measure of ∠DEA is 50. Let's notice that angles ∠DEA and ∠CEB are congruent as they are vertical angles. Therefore, the measure of ∠CEB is also 50.