Question

In PQR angle P=2 angle Q and 2 angle R =3 angle Q,calculate the angles of triangle PQR

Answer 1

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Given,

$∠P=2∠Q$

$∠R=3∠Q$

$We \: know \: that \: in \: △PQR$

$∠P+∠Q+∠R=180$

$2∠Q+∠Q+3∠Q=180$

$6∠Q=180$

$∠Q= \frac{180}{6} = {30}^{o}$

$∠P=2∠Q= {60}^{o}$

$∠R=3∠Q= {90}^{o}$

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Answer 2

Answer:

/_P = 80°, /_Q = 40° and /_R = 60°

Step-by-step explanation:

Given that In ∆PQR /_P = 2/_Q, 2/_R = 3/_Q

We need to find out the angles of ∆PQR.

We know that sum of all angles of triangle is 180°>

So,

/_P + /_Q + /_R = 180°

Substitute the values,

→ 2/_Q + /_Q + (3/_Q)/2 = 180°

→ 4/_Q + 2/_Q + 3/_Q = 360°

→ 9/_Q = 360°

Divide by 5 on both sides,

→ (5/_Q)/5 = 180°/5

→ /_Q = 40°

Hence, the value of /_Q is 40°.

Similarly,

/_P = 2/_Q = 2(40°) = 80°

2/_R = 3/_Q = 3(40°)/2 = 120°/2 = 60°

Therefore, the angles of triangle PQR is 80°, 40° and 60°.