Question : The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of $∠ P S R$ is:
Option 1: $30^{\circ}$
Option 2: $15^{\circ}$
Option 3: $60^{\circ}$
Option 4: $45^{\circ}$

Question

Question : $△ A B C$ is an equilateral triangle. The side $B C$ is produced to point $D$ . If $A$ joines $D$ and $B C = C D$ , then the degree measure of angle $C A D$ is equal to:
Option 1: $30^{\circ}$
Option 2: $15^{\circ}$
Option 3: $45^{\circ}$
Option 4: $18^{\circ}$

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Answer 1

Correct Answer: $30^{\circ}$

Solution :

Given: $P Q R$ is an equilateral triangle and $Q R = R S$
$\Rightarrow ∠ P R S = 180^{\circ} - 60^{\circ} = 120^{\circ}$
We have, $P R = R Q$ and $R Q = R S$ , it follows that $R S = P R$
$∴ ∠ P S R = ∠ R P S$
The sum of angles in a triangle is $180^{\circ}$ .
$\Rightarrow ∠ P S R + ∠ R P S + ∠ P R S = 180^{\circ}$
$\Rightarrow 2 ∠ P S R = 180^{\circ} - ∠ P R S = 180^{\circ} - 120^{\circ}$
$\Rightarrow 2 ∠ P S R = 60^{\circ}$
$∴ ∠ P S R = 30^{\circ}$
Hence, the correct answer is $30^{\circ}$ .

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Question : The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is:Option 1: 30∘Option 2: 15∘Option 3: 60∘Option 4: 45∘

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Question : The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of $∠ P S R$ is:
Option 1: $30^{\circ}$
Option 2: $15^{\circ}$
Option 3: $60^{\circ}$
Option 4: $45^{\circ}$