The first angle of a triangle is one-third its second angle, where the third angle is 5 times the first angle. Find the measures of all the angles of the triangles.

Sub Grade: 9

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20°, 40°, 60°

10°,20°,40°

20°, 60°, 100°

10°, 40°, 60°

answer is C.

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Detailed Solution

Let the three angles of the triangle
Be θ ,θ2 and θ3
The first angle is one- third of the second.
∴ θ1 = θ2 / 3 ..(1)
also , third angle is 5 time the first
∴ θ3 =5X θ1
Putting value of θ1 from equation 1 , we get
θ3 = 5 X θ2 / 3 ..(2)
We know that, the sum of all interior angle of a triangle is 180 °
∴ θ1 + θ2 + θ3 = 180°
Putting the value of θ1 and θ3 from (1) and ( 2) ,we get
θ2 / 3 +θ2 +5 X θ2 / 3 =180°
θ2 = 60°
θ1 = 60° / 3 =20° [∴ from (1)]
θ3 = 5X 60° / 3 = 100° [∴ from (2)]
hence , the angle of triangle are
20 , 60 an 100

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