Question

One of the exterior angles of a triangle is 100° nd the interior opposite angles are in the ratio 2:3.find the angle of a triangle

Answer 1

Let the interior opposite angles be 2x and 3x
2x+3x=100
5x=100
x=100/5
x=20
2x=2(20)=40
3x=3(20)=60

Answer 2

Let the common ratio be x.

Then, interior opposite angles=2 x and 3 x

Exterior angle =100°

Using exterior angle property that states that the sum of interior opposite angles gives the value of exterior angle

So,

exterior angle = sum of interior opposite angles

100°=2x+3x

100°=5x

100°/5=x

20°=x

So, interior opposite angles are

2x =2×20°

= 40°

and 3× 20°=60°

angle remaining + exterior angle = 180° (Linear pair)

let the angle remaining be y.

y+100°=180°

y=180°-100°

y=80°

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