Question

From the given figure find the value of y

Answer 1

From the figure,

∠ACB = ∠XCY  ...[Vertically opposite angles]

ACB = 48°  ...(1)

In ∆ABC, ∠CBD is the exterior angle at B

Exterior angle = Sum of interior opposite angles

∠CBD = ∠BAC + ∠ACB

∠CBE + ∠EBD = 57° + 48°

65° + ∠EBD = 105°

∠EBD = 105° + 65° = 40° ...(2)

In ∆EBD, y is the exterior angle at D.

y = ∠EBD + ∠BED ...[∵ Exterior angle = Sum of opposite interior angles]

y = 40° + 97° ...[∵ From (2)]

y = 137°