Question

Angles of a triangle ABC are in the ratio 1:2:3. If PQRis a triangle whose sides are double the corresponding sides of triangle ABC then find the measure of angles of triangle PQR.

Answer 1

sum of angles of a triangle = 180
so 1x + 2x + 3x = 180
   6x = 180  =>  x = 180/6  =>  30
   therefore x = 30
  so , 1x = 30
     2x = 60
     3x = 90
now , in the doubled sided triangle PQR , the sum of angles of triangle = 180
  either if the sides are doubled , so , 2AB = PQ
   2BC = QR
2 AC = PR
so, the ratio of side is equal i.e  2:1
so the angles will be equal so the measure of angles of triangle PQR are,
     30 , 60 , 90 .

Answer 2

Step-by-step explanation:

Angles are in the ratio =1:2:3

Let the angles be x,2x,3x

Sum of angles =180

x+2x+3x=180

6x=180

x=30

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Hence, the angles are 30

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,60

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,90

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The triangle is a right angled triangle.