In the given figure, ∠ABD = 55° and ∠ACD = 30°, If ∠BAC = y° and non-reflex ∠BDC = x°, then what is the value of (x - y)?

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 5 Jan 2021 Shift 1)

Answer 1

Given:

F4 SSC Savita 29-01-24 D3

∠ABD = 55° and ∠ACD = 30°

Calculation:

∠BAD = α and ∠CAD = β

So, ∠BAC = y = α + β

So Referring to the triangle ΔABD and ΔACD,

∠ADB = 180°- α - 55°

∠ADC = 180°- β - 30°

For point D,

∠ADB +∠ADC + x = 360°

⇒ 180°- α - 55° + 180°- β - 30° + x = 360°

⇒ 360 - α - β - 85° + x = 360

⇒ x - (α + β) - 85° = 0

⇒ x - y - 85° = 0

⇒ x -y = 85°

∴ The correct answer is option (1).

Download Solution PDF