Question

An exterior angle of a triangle is 120o

and the two interior opposite angles are equal. Find each of

these angles.​

Answer 1

$\sf{\huge{\underline{\orange{Given :-}}}}$

• An exterior angle of a triangle is 120°.

• The two interior opposite angles are equal.

$\sf{\huge{\underline{\red{To\:Find :-}}}}$

• Each of these angles.

$\sf{\huge{\underline{\pink {Solution :-}}}}$

Let the two interior opposite angles be 'x' .

We know that the opposite angles inside a triangle.

We have an exterior angle = 120°

We know that,

Sum of opposite interior angles = Exterior angle

➝ x + x = 120°

➝ 2x = 120°

➝ x = 120°/2

➝ x = 60°

The two angles are 60°

Using the angle sum property of triangles ,

x + x + c = 180°

➝ 60° + 60° + c = 180°

➝ 120° + c = 180°

➝ c = 180° - 120°

➝ c = 60°

Each angles are of 60°, Hence the triangle is an equilateral triangle.

____________________________________

Answer 2

Answer:

Let the two interior opposite angles be 'x' .

We know that the opposite angles inside a triangle.

We have an exterior angle = 120°

We know that,

Sum of opposite interior angles = Exterior angle

➝ x + x = 120°

➝ 2x = 120°

➝ x = 120°/2

➝ x = 60°

The two angles are 60°

Using the angle sum property of triangles ,

x + x + c = 180°

➝ 60° + 60° + c = 180°

➝ 120° + c = 180°

➝ c = 180° - 120°

➝ c = 60°

Each angles are of 60°, Hence the triangle is an equilateral triangle.

hope this helps you