Question

One angle of a triangle is 60°. The other two angles are in ratio 5 : 7 .​

Answer 1

To find : two angles of triangle, given in ratio .

Given : ∠A $= 60$° , ratio of other two angles = $5 : 7$

Solution :

• Let, ∠A , ∠B, ∠C be the three angles of triangle.

• Let , two angles ∠B, ∠C be $5x$ and $7x$ respectively .
• Therefore according to angle sum property of triangle , we know that sum of all the three angles is $180$°.

             i.e. ∠A + ∠B +  ∠C = $180$°

• Substituting the values : $60 + 5x + 7x = 180$°

                                                       $60 + 12x = 180$°

                                                               $12x = 120$°

                                                                  $x = 10$°

• Now to find ∠B :

          ∠B $= 5x = 5 ( 10 )$ $= 50$°

• To find  ∠C :

         ∠C $= 7x = 7 ( 10 )$ $= 70$°

Hence , two angles of triangle in ratio are $50$° and $70$°.

Answer 2

The measure of one angle is  60°

The other two angles are in the ratio of 5 : 7

Let the other two angles be 5x and 7x

We know that sum of angles in a triangle is 180°

So, 60 + 5x + 7x = 180

              5x + 7x = 180 - 60

                       12x = 120

                            x = 120/ 12

                             x = 10

So, 5x = 5 × 10

          = 50

    7x = 7 × 10

        = 70

Hence, the two angles will be 50° and 70°