Question

Refer the attachment and some one give the correct answer with correct explanation please.​

Answer 1

Required Answer:

→ Option A ( 72° )

Given:

In ∆PQR :

• PQ = QR

This means it is an isosceles triangle as 2 two sides of this triangle are equal.

• Angle Q is twice the Angle P.

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To calculate:

• Angle Q = ?

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Calculation:

Let us assume the measure of $\angle$ P as x°.

Therefore,

• $\angle$ Q becomes 2x°.

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As it is an isosceles triangle, so

• Angles opposite to equal sides will be equal.

Therefore,

⇒ $\angle$ Q = $\angle$ R

Measure of $\angle$ R is also 2x°.

Now, by using the angle sum property of triangle:

• Sum of interior angles of ∆ = 180°

⇒ $\angle$ P + $\angle$ Q + $\angle$ R = 180°

⇒ x° + 2x° + 2x° = 180°

⇒ 5x° = 180°

⇒ x° = 180°/5

⇒ x° = 36

Therefore, $\angle$ Q = 2x°

⇒ $\angle$ Q = ( 2 × 36 )°

⇒ $\angle$ Q = 72°

Value of $\angle$ Q is 72°.