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Question
From the given figure find the value of y
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Solution
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°
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