Question
Download Solution PDFIn the diagram, M is the midpoint of
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFIn ΔXYM,
∠XYM + ∠XMY + ∠YXM = 180°
⇒ 16° + (180° – ∠XMZ) + ∠YXM = 180° (∵ ∠XMY + ∠XMZ = 180°)
⇒ 16° + 180° – 32° + ∠YXM = 180°
⇒ ∠YXM = 16° = ∠XYM
∴ YM = XM = MZ (∵ M is the midpoint of YZ)
∴ ∠MXZ = ∠MZX = ∠XZY
In ΔXMZ
∠XMZ + ∠MXZ + ∠MZX = 180°
⇒ 32° + ∠MXZ + ∠MXZ = 180°
⇒ 2 × ∠MXZ = 180° – 32°
⇒ ∠MXZ = 74°
⇒ ∠XZY = ∠MXZ = 74°
∴ The value of ∠XZY is 74°
Last updated on Jul 11, 2025
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