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In the diagram below, ABCD is a parallelogram, AB is extended through B to E, and CE is drawn.If CE? BE and

In The Diagram Below ABCD Is A Parallelogram AB Is Extended Through B To E And CE Is DrawnIf CE BE And class=

Sagot :

The opposite angles of a parallelogram are congruent. This means that

angle D = angle B

angle A = angle C

If angle D is 124 degrees, then

angle B = 124 degrees

Recall, the sum of the angles on a straight line is 180 degrees. These angles are also called linear pairs. This means that

angle ABC and angle EBC are linear pairs

angle ABC + angle EBC = 180

124 + angle EBC = 180

angle EBC = 180 - 124 = 56 degrees

If line CE = line BE, it means that triangle EBC is an isosceles triangle because it has two congruent sides. In an isosceles triangle, the base angles are congruent. This means that

angle ECB and angle EBC are congruent

Thus,

angle ECB + angle EBC = 56 degrees

The sum of the angles in a triangle is 180 degrees. This means that

angle ECB + angle EBC + angle BEC = 180

56 + 56 + angle BEC = 180

112 + angle BEC = 180

angle BEC = 180 - 112

angle BEC = 68 degrees

Thus, the correct option is

3) 68 degrees

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