Question

in PQR angle P= 4/3, angle Q= 2 angle R find the measure of the three angles of the triangle​

Answer 1

Step-by-step explanation:

let angle R = x

angle Q = 2R = 2x

angle P = 4/3 Q = 4/3 × 2x = 8x/3

sum of all angles of triangle = 180

$x + 2x + \frac{8x}{3} = 180 \\ \frac{3x + 6x + 8x}{3} = 180 \\ 17x = 180 \times 3 \\ 17x = 540 \\ x = \frac{540}{17} \\ x = 31.8$

angle R = x = 31.8

angle Q = 2x = 2 × 31.8 = 63.6

angle P = 4/3 Q = 4/3 × 63.6 = 4 × 21.2 = 84.8

hope you get your answer

Answer 2

Given,

$\angle P=\frac{4}{3}\angle Q\\\angle Q=2\times \angle R\\\therefore \angle P=\frac{4}{3}\times 2\angle R=\frac{8}{3}\angle R$

We know that the sum of all angles in a triangle is 180°

$\therefore \angle P+\angle Q+\angle R=180\°\\\frac{8}{3} \angle R +2\angle R+\angle R=180\°\\(\frac{8+6+3}{3})\angle R=180\°\\\frac{17}{3}\angle R=180\°\\\angle R=31.76\°\\\therefore \angle Q=63.53\°\\\therefore \angle P=84.71\°$

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