Question

An exterior angle of a triangle is 100 degree and its interior opposite angles are in ratio 2:3 find all the angles

Answer 1

exterior angle is the sum of the 2 opposite interior angles

Given that the exterior angle is 100º

⇒ Sum of the two opposite angles = 100º

Define x:

The two angles are in the ratio 2 : 3

Let x be the constant ratio

The two angles are 2x : 3x

Solve x:

Given that the sum is 100

2x + 3x = 100

5x = 100

x = 20

Find the two angles:

2x = 2(20) = 40º

3x = 3(20) = 60º

Find the third angle:

Sum of a triangle is 180º

third angle = 180 - 40 - 60 = 80º

Answer: The angles are 40º, 60º and 80º

Answer 2

THE EXTERIOR  ANGLE = 100

AND ITS OPPOSITE INTERIOR ANGLE 2:3

SO, 2:3 = 100 [ EXTERIOR ANGLE IS EQUAL TO OPPOSITE INTERIOR ANGLE]

2X+3X = 100

5X = 100

X= 20

2X = 2[20] = 40

3X = 3[20] = 60

AND LAST ANGLE ==>

40+60+X = 180 [ SUM OF ALL ANGLE IN A TRIANGLE IS 180]

100+ X = 180

X = 80

I HOPE ITS HELPFUL