Question

one of the exterior angles of a triangle is 120° and the interior opposite angles of it are in the ratio 4 : 2. Find the angles of the triangle.



60°,60°,60°

70°,50°,60

80°,40°,60°

75°,45°,60°




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Answer 1

Answer:

The angles are 80, 40, 60

Step-by-step explanation:

Let the opposite angles be 4x and 2x

4x+2x=120 (Exterior angle property)

6x=120

x=20

4x=80

2x=40

The first to angles are 80 and 40

Let the third angle be 'a'

80+40+a=180 (angle sum property)

120+a=180

a=180-120

a=60

Hence the angles are 80, 40, 60

Answer 2

Given - Exterior angle of triangle = 120°

Interior opposite angle = 4:2

Find - All the angles of triangle.

Solution - Firstly applying exterior angle property as per the given information.

Let the interior opposite angles be 4x and 2x.

Now, as per the exterior angle property, we will get equation as follows-

4x + 2x = 120

6x = 120

x = 20°

Therefore, 4x = 4*20

Interior opposite angle 1 = 80°

2x = 2*20

Interior opposite angle 2 = 40°

Further, we know all angles of triangle sum up to 180°.

Thus, let us assume the third angle of triangle be y.

Now, 80 + 40 + y = 180

120 + y = 180

y = 180 - 120

y = 60°

Hence, the angles of triangle are 80°,40°,60°