In parallelogram LOST, SN⊥OL and SM⊥LT. Find ∠STM, ∠SON and ∠NSM.
Solution:
Given, LOST is a parallelogram.
SN⊥OL and SM⊥LT
We have to find ∠STM, ∠SON and ∠NSM.
From the figure, ∠MST = 40°
In triangle STM,
By angle sum property of a triangle,
∠MST + ∠STM + ∠MTS = 180°
40° + ∠STM + 90° = 180°
∠STM = 180° − 130°
∠STM = 50°
We know that the opposite angles of a parallelogram are equal.
∠STM = ∠SON
So, ∠SON = 50°
In triangle SON,
By angle sum property of a triangle,
∠SON + ∠NSO + ∠SNO = 180°
50° + ∠NSO + 90° = 180°
∠NSO = 180° − 140°
∠NSO = 40°
We know that the adjacent angles of a parallelogram are supplementary.
So, ∠SON + ∠OST = 180°
From the figure,
∠SON + ∠NSO + ∠NSM + ∠MST = 180°
50° + 40° + ∠NSM + 40° = 180°
90° + 40° + ∠NSM = 180°
130° + ∠NSM = 180°
∠NSM = 180° - 130°
Therefore, ∠NSM = 50°
✦ Try This: In Rhombus LOST, SN⊥OL and SM⊥LT. Find ∠STM, ∠SON and ∠NSM
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 153
In parallelogram LOST, SN⊥OL and SM⊥LT. Find ∠STM, ∠SON and ∠NSM.
Summary:
In parallelogram LOST, SN⊥OL and SM⊥LT. The values of ∠STM, ∠SON and ∠NSM are 50°, 50° and 50°.
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