CTET 1 Mar 2026 Paper 1, Question 32

Topic: Geometry

Q32

In $\Delta ABC$ , sides BC and BA are produced to D and E, respectively. If $\angle ACD = 120^\circ$ and $\angle CAE = 130^\circ$ , then what is the measure of $\angle ABC$ ?

(1) $65^\circ$
(2) $70^\circ$ Correct answer
(3) $75^\circ$
(4) $80^\circ$

Solution.

CBSE answer: (2)

Answer: (2) $70^\circ$

$\angle ACB = 180^\circ - 120^\circ = 60^\circ$ (linear pair at C).
$\angle BAC = 180^\circ - 130^\circ = 50^\circ$ (linear pair at A).
$\angle ABC = 180^\circ - 60^\circ - 50^\circ = 70^\circ$ .
Check: exterior $\angle ACD = \angle A + \angle B = 50^\circ + 70^\circ = 120^\circ$ .