Question

If the angles of a triangle are in the ratio 7:8:5, then what is the difference between
the greatest and the smallest angle?

Answer 1

Answer :

• Greatest angle is 72⁰
• Smallest angle is 45⁰

Given :

• The angles of a triangle are in the ratio 7 : 8 : 5

To find :

• Greatest and smallest angles

Solution :

Given that, The angles of a triangle are in the ratio is 7:8:5 so,

• Let the angles of a triangle be 7x , 8x and 5x

As we know that,

• Sum of angles of a triangle is equal to 180⁰

》 7x + 8x + 5x = 180⁰

》20x = 180

》x = 180/20

》x = 9

• 7x = 7(9) = 63⁰
• 8x = 8(9) = 72⁰
• 5x = 5(9) = 45⁰

• Greatest angle is 72⁰
• Smallest angle is 45⁰

Hence , Greatest and smallest angle is 72⁰ and 45⁰

Method (2) :

As we know that,

• sum of angles of a triangle is equal to 180⁰

Given that , 7 : 8 : 5 ratio

》Ratio = 7 + 8 + 5 = 20

Now,

• Smallest angle = 5/20 × 180 = 45⁰
• Greatest angle = 8/20 × 180 = 72⁰