Question

In triangle pqr, if 3 angle P =4 angle Q=6 angle R, find angle P, angle Q and angle R​

Answer 1

Answer:

If 3∠P=4∠Q=6∠R then ∠R = 40° , ∠P  = 80°  and ∠Q = 60°.

Step-by-step explanation:

As per given condition

3∠P=4∠Q=6∠R ----- (1)

The sum of angles of the triangle is 180°.

In triangle PQR,

∠P+∠Q+∠R=180°

⇒ $\frac{6}{3}$ ∠R+ $\frac{6}{4}$∠R+∠R=180°   ----- (1)

⇒ $(\frac{6}{3} +\frac{6}{4} + 1)$ ∠R=180°

⇒ $\frac{6(4) + 6(3) + 12}{12}$∠R=180°

⇒ $\frac{24 + 18 + 12}{12}$∠R=180°

⇒ $\frac{54}{12}$∠R=180°

⇒ ∠R=180°   $\frac{12}{54}$

⇒ ∠R=

$180 \times \frac{2}{9} \\= 20 \times 2\\= 40$

So,  ∠R= = 40°

∠P = 2R = 40(2) = 80°

∠Q=$\frac{6}{4}$∠R = 60°