Question

one angle of a triangle is 60 degree the other two angles are in the ratio 5:7 find the two angles​

Answer 1

One angle of a triangle is 60 degree the other two angles are in ratio 5:7. The two angles are 50° and 70°.

Stepwise explanation is given below:

- Measure of one of the angle of a triangle = 60°.

- Other two angles are in the ratio 5:7

- Let the other two angles be 5x and 7x.

- So, we know the sum of the angles of a triangle is 180°.

then, 5x+7x+60° = 180°

12x+60° = 180°

12x = 180° - 60°

12x = 120°

x = 120/12

x = 10°

so, the measure of other two angles will found by putting the value x = 10 is :-

=5x = 5*10 = 50°

And, 7x = 7*10 = 70°

Answer 2

Given :

For a Triangle ,

One angle of triangle = 60°

The ratio of other two angles = 5 : 7

To Find :

The other two angles

Solution :

For A Triangle

The Sum of all three angles of Triangle = 180°

Let ∠ A , ∠B , ∠C  are three angles of Triangle ABC

let  ∠ A =  60°

And ∠ B = 5 x°

And ∠ C = 7 x°

∵    ∠ A + ∠B + ∠C  =   180°         ...........1

Put the value of ∠ A , ∠B , ∠C  in eq 1

So,   60° +  ∠B + ∠C  =   180°

Or,     ∠B + ∠C  =   180° -  60°

Or,    ∠B + ∠C  =   120°

Or,     5 x° +  7 x° = 120°

Or,              12 x° = 120°

∴                    x = $\dfrac{120}{12}$

i.e                 x= 10°

So, The value of  ∠ B = 5 x° = 5 × 10° = 50°

And The value of ∠ C = 7 x° = 7 × 10° = 70°

Hence, The measure of other two angles of Triangle is  50°  ,  70°  Answer