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Question
In parallelogram LOST, SN ⊥ OL and SM ⊥ LT. Find ∠STM, ∠SON and ∠NSM.
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Solution
Given, ∠MST = 40°
In ΔMST,
By the angle sum property of a triangle,
∠TMS + ∠MST + ∠STM = 180°
⇒ ∠STM = 180° – (90° + 40°) ...[∵ SM ⊥ LT, ∠TMS = 90°]
= 50°
∴ ∠SON = ∠STM = 50° ...[∵ Opposite angles of a parallelogram are equal]
Now, In the ΔONS,
∠ONS + ∠OSN + ∠SON = 180° ...[Angle sum property of triangle]
∠OSN = 180° – (90° + 50°)
= 180° – 140°
= 40°
Moreover, ∠SON + ∠TSO = 180° ...[∵ Adjacent angles of a parallelogram are supplementary]
⇒ ∠SON + ∠TSM + ∠NSM + ∠OSN = 180°
⇒ 50° + 40° + ∠NSM + 40° = 180°
⇒ 90° + 40° + ∠NSM = 180°
⇒ 130° + ∠NSM = 180°
⇒ ∠NSM = 180° – 130° = 50°
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