Question

In triangle PQR, QR=PQ and angle Q=40°. Find the measure of angle P​

Answer 1

Step-by-step explanation:

QR=PQ

so the triangle is isosceles...

so..

<QPR=<QRP=x

Sum of the interior angles of a triangle is 180°

so <RQP+<QPR+<PRQ=180°

=>2x+40°=180°

=>2x=180-40

=>x=140/2

=>x=70°

so <QPR=x

so <P=70°

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Answer 2

Given:

• QR = PQ
• ∠Q = 40°

To Find:

• The value of angle P.

Solution:

It is given that QR=PQ, therefore we can say that the triangle PQR is an isosceles triangle.

∴∠R = ∠P

Now using the sum of triangles rule we can write,

⇒ ∠P+∠Q+∠R = 180°

⇒ ∠P+∠P+∠Q = 180° {since, ∠R = ∠P}

⇒ 2∠P+∠Q = 180°

On substituting the given values in the above formula we get

⇒ 2∠P+40 = 180°

⇒ 2∠P = 180-40 {subtracting the terms}

⇒ 2∠P = 140° {shifting of numericals to one side to get the equation in terms of "P".}

⇒ ∠P = 140/2 = 70° {dividing the terms}

∴ The value of angle P = 70°