In the figure below, A, D, C, and E are collinear. AD, BD, and BC are all the same length

In the figure below, A, D, C, and E are collinear. AD, BD, and BC are all the same length, and the angle measure of ∠ABD is as marked. What is the degree measure of ∠BCE ?

1. 50°
2. 100°
3. 105°
4. 130°
5. 160°

Answer

The correct answer is D.

Because BD = AD, ∆ABD is isosceles, so its base angles are congruent.

Therefore, ∠BAD = ∠ABD = 25°.

Because the sum of the angle measures in ∆ABD must equal 180°,

∠ADB = 180° - (25° + 25°) = 130°

Because ∠ADB and ∠BDC are a linear pair, ∠BDC = 180° - 130° = 50°.

Because BD = BC, ∆DBC is isosceles, so its base angles are congruent.

∠BCD = ∠BDC = 50°.

Finally, ∠BCD and ∠BCE are a linear pair, so

∠BCE = 180° - 50° = 130°