Question

Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points A and E. They are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees. Given: Line BC is parallel to line ED, m∠ABC = 70°, m∠CED = 30°. Prove: m∠BEC = 40°. Which of the following accurately completes the missing statement and justification of the two-column proof?

1) m∠ABC = m∠CED; Corresponding Angles Theorem
2) m∠ABC = m∠CED; Alternate Interior Angles Theorem
3) m∠ABC = m∠BED; Corresponding Angles Theorem
4) m∠ABC = m∠BED; Alternate Interior Angles Theorem

Answer 1

To prove that angle BEC measures 40 degrees, we can use the Alternate Interior Angles Theorem. According to this theorem, if two lines are parallel to each other, then the alternate interior angles formed by a transversal are congruent. By applying this theorem, we find that angle BEC measures 110 degrees.

Step-by-step explanation:

To solve the problem, we can use the Alternate Interior Angles Theorem. According to this theorem, if two lines are parallel to each other, then the alternate interior angles formed by a transversal are congruent. In this case, angle ABC and angle CED are alternate interior angles. Since angle ABC measures 70 degrees, angle CED also measures 70 degrees.

Now, we know that angle CED is an exterior angle of triangle BEC. And the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. So, in this case, we can say that angle CED + angle BEC = 180 degrees.

Since angle CED is 70 degrees, we can substitute it in the equation: 70 degrees + angle BEC = 180 degrees. Simplifying the equation, we find that angle BEC = 110 degrees. Therefore, the missing statement and justification for the two-column proof is: m∠ABC = m∠CED; Alternate Interior Angles Theorem.