Question

An exterior angle of a triangle measures 120 and its interior opposite angles are in a ratio of 7:5

Answer 1

Attachment solution :-

Let the interior angles of a triangle be

a , b and c

Here,

Angle a + 125° = 180° [ L. P]

Angle a = 180° - 125°

Angle a = 55°

Now,

Angle b + 125° = 180° [L.P]

Angle b = 180° - 125°

Angle b = 55°

By using angle sum property,

Angle a + Angle b + Angle c = 180°

Subsitute the required values,

55° + 55° + Angle c = 180°

110° + Angle c = 180°

Angle c = 180° - 110°

Angle c = 70°

Now,

Angle c + x = 180° [ L. P]

70° + x = 180°

x = 180° - 70°

x = 110°

Hence, The value of x is 110°

Solution :-

Here ,

The two interior opposite angle are given in ratio 7 : 5

Let the given ratio be 7x and 5x

Now,

As we know that ,

The sum of two interior opposite angle is equal to the exterior angle

Therefore,

7x + 5x = 120°

12x = 120°

x = 120/12

x = 10°

Thus, The value of x is 10°

Therefore,

The first angle = 7 * 10° = 70°

The second angle = 5 × 10° = 50°

Now,

As we know that,

The sum of angles of a triangle is 180°

Let the third angle be y

Therefore,

70° + 50° + y = 180°

120° + y = 180°

y = 180° - 120°

y = 60°

Hence, The all angles of a triangle are 70° , 50° and 60° $.$

Answer 2

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Here ,

The two interior opposite angle are given in ratio 7 : 5

Let the given ratio be 7x and 5x

Now,

As we know that ,

The sum of two interior opposite angle is equal to the exterior angle

Therefore,

7x + 5x = 120°

12x = 120°

x = 120/12

x = 10°

Thus, The value of x is 10°

Therefore,

The first angle = 7 * 10° = 70°

The second angle = 5 × 10° = 50°

Now,

As we know that,

The sum of angles of a triangle is 180°

Let the third angle be y

Therefore,

70° + 50° + y = 180°

120° + y = 180°

y = 180° - 120°

y = 60°

Hence, The all angles of a triangle are 70° , 50° and 60°

⠀⠀⠀⠀●●●Hope it helps●●●

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