In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
Solution:
Given, FIST is a parallelogram.
We have to find ∠SFT, ∠OST and ∠STO.
Since FT ║SI with TI as transversal, the alternate interior angles are equal.
So, ∠TIS =∠ITF
Similarly, ∠TIF =∠ITS
From the figure,
∠ITS =∠OTS = ∠STO and ∠ITF = ∠OTF
So, ∠STO = 35°
From the figure,
∠FOT = 110°
We know that the linear pair of angles are supplementary.
So, ∠FOT + ∠TOS = 180°
∠TOS = 180° - 110°
= 70°
In triangle SOT,
∠STO = 35°
∠TOS = 70°
By angle sum property of a triangle,
∠OST + ∠STO + ∠TOS = 180°
∠OST = 180° - [35° + 70°]
∠OST = 75°
In triangle FOT,
∠OTF = 25°
∠FOT = 110°
By angle sum property of a triangle,
∠OFT + ∠OTF + ∠FOT = 180°
∠OFT = 180° - (110° + 25°)
∠OFT = 45°
From the figure,
∠OFT = ∠SFT
Therefore, ∠SFT = 45°
✦ Try This: In Rhombus FIST, find ∠SFT, ∠OST and ∠STO.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 149
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
Summary:
In parallelogram FIST, ∠SFT, ∠OST and ∠STO are 45°, 75° and 35°.
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