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CAT 2001 — QA Question 33

Basics of TrianglesEasy

In ∆DEF shown below, points A, B, and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If ∠D = 40°, then what is ∠ACB in degrees?

Answer & solution

  • A

    140

  • B

    70

  • 100

  • D

    None of these

Solution

At point C,

(180° − 2x) + z + (180° − 2y) = 180°

z = 2x + 2y − 180° = 2(x + y) − 180°                               ...(i)

Also, in ΔDEF, x + y + 40° = 180°

x + y = 140°

Substituting in equation (i), we get,

z = 2 × 140 − 180 = 100°

Hence, option (c).

CAT 2001 QA Q33: In ∆DEF shown below, points A, B, and C are taken on DE, DF and EF respectively such that EC = AC and CF = B — Solution | TheCATExam