ABCD is a parallelogram in which ∠ ACB = 40°, ∠ BAC = 80°, then ∠ ADC is

Question

Question

This question was previously asked in

Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 2)

Answer 1

Concept -

(1) In parallelogram ABCD, opposite angles are congruent.
(2) Also, the angles in triangle ABC must sum to 180°
m∠ACB + m∠BAC + m∠CAB = 180°

Explanation -

ABCD is a parallelogram ∠ACB = 40° and ∠BAC = 80°

Substitute the known angle measures:
40° + 80° + m∠CBA = 180°
m∠CBA = 180° - 40° - 80° = 60°

From (1), opposite angles are congruent.
Therefore, the measure of m∠ADC = 60°

Hence the correct answer is ∠ ADC = 60°