Question

one of the exterior angles of a triangle is 125 degress and the interior opposite angles are in the ratio 2:3. Find the angles of the triangle​

Answer 1

Step-by-step explanation:

Given :-

One of the exterior angles of a triangle is 125 degress and the interior opposite angles are in the ratio 2:3.

To find :-

Find the angles of the triangle?

Solution:-

Given that

The exterior angle of a triangle = 125°

The ratio of the interior opposite angles of the exterior angle = 2:3

Let they be 2X° and 3X°

We know that

An exterior angle of a triangle is equal to the sum of the interior opposite angles .

=> 2X° + 3X° = 125°

=> 5X° = 125°

=> X° = 125°/5

=> X° = 25°

Now, 2X° = 2(25°)=50°

3X°=3(25°)=75°

Answer:-

The interior opposite angles are 50° and 75°

Check:-

The interior opposite angles are 50° and 75°

Their sum = 50°+75°=125°

Verified the given relation.

Used formulae:-

• An exterior angle of a triangle is equal to the sum of the interior opposite angles .

Answer 2

$\: \: \underline{{ \red { \underline{{ \huge{ \mathtt{A}}}}}}{ \gray{ \underline{{ \mathtt{NSWER :-}}}}}}$

---------------------------------------------

We know that,

Exterior angle = Sum of opposite interior angles

---------------------------------------------

Let the opposite interior angles be 2x and 3x .

➜ Exterior angle = 2x + 3x

➜ 125° = 5x

➜ 125/5 = x

➜ x = 25°

---------------------------------------------

Now,

Opposite interior angles are,

➜ 2x = 2 × 25° = 50°

➜ 3x = 3 × 25° = 75°

---------------------------------------------

Required Answer :-

➜ 50° and 75°

---------------------------------------------

Verification :-

➜ 50° + 75° = 125°

---------------------------------------------

Property used :-

➜ An exterior angle is equal to the sum of its opposite interior angles.

---------------------------------------------