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CAT 1996 — QA Question 3

Basics of QuadrilateralsEasy
Passage / Data

Direction: Answer the questions based on the following information.

In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

AB = 2 km  AC = 2km  AD > 2 km  AE > 3 km BC = 2 km
BD = 4 km  BE = 3 km CD = 2 km CE = 3 km  DE > 3 km

If ABCD is a square and BCE is an equilateral triangle, what is the measure of ∠DEC?

Answer & solution

  • 15°

  • B

    30°

  • C

    20°

  • D

    45°

Solution

Since ΔBCE is an equilateral triangle, CE = BC = BE.
And since ABCD is a square, BC = CD. Hence, CD = CE.
So in ΔCDE, we have CD = CE. Hence, ∠EDC = ∠CED.
Now ∠BCE = 60° (since equilateral triangle) and ∠BCD = 90° (since square).
Hence, ∠DCE = ∠DCB + ∠BCE = (60 + 90) = 150°.
So in ΔDCE, ∠EDC + ∠CED = 30° (since three angles of a triangle add up to 180°). Hence, we have ∠DEC = ∠EDC = 15°.

CAT 1996 QA Q3: If ABCD is a square and BCE is an equilateral triangle, what is the measure of ∠DEC? — Solution | TheCATExam