Question : In the given figure, PQRS is a square and SRT is an equilateral triangle. What is the value of $\angle SOR ?$
Option 1: $45^{\circ}$
Option 2: $55^{\circ}$
Option 3: $60^{\circ}$
Option 4: $75^{\circ}$
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Correct Answer: $75^{\circ}$
Solution :
Given: PQRS is a square and SRT is an equilateral triangle.
$\angle SRO=60^{\circ}$ (angle of equilateral triangle)
⇒ $\angle RSQ=\angle RSO=45^{\circ}$ (angle of diagonal of the square)
In $\triangle SOR$,
⇒ $\angle SOR+\angle SRO+\angle RSO=180^{\circ}$
⇒ $\angle SOR=180^{\circ}-\angle SRO-\angle RSO$
Putting the values, we get:
⇒ $\angle SOR=180^{\circ}-60^{\circ}-45^{\circ}$
Thus, $\angle SOR=75^{\circ}$
Hence, the correct answer is $75^{\circ}$.
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