Question

please help me with this question​

Answer 1

Answer:

Given: As SN⊥OL  & SM⊥LT, ∠SNO=∠SNL= 90°  & ∠SMT=∠SML=90° ; ∠MST= 40°

∠STM:

∠STM= 180-(∠TSM+∠SMT) → ( Angle Sum Property Of Δ)

∠STM= 180-(40+90) → ( From Given )

∠STM= 180-130

∴∠STM= 50°

∠SON:

∠SON = ∠STM = 50° → (Opposite angles in a parallelogram are equal)

∠NSM:

As ∠LOS = ∠OST

Let ∠LOS = x  And ∠OST = x

x+50+x+50 = 360  → ( Angle sum property of a quadrilateral )

2x+100 = 360

2x = 360-100

x = $\frac{260}{2}$

∴ x = 130°

∴ ∠NSM= 130°

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