Question

GD If the angles of a triangle are in the ratio 2:3 : 4, then find the difference between the
greatest and the smallest angles.
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Answer 1

Answer :

• Greatest angle = 80⁰
• Smallest angle = 40⁰

Given :

• If the angles of a triangle are in the ratio 2:3:4

To find :

• Different between the greatest and the smallest angles

Solution :

Given , the angles of a triangle are in the ratio 2:3:4 so,

• Let the angles of triangle be 2x , 3x and 4x

We know that

• Sum of angles of a triangle is equal to 180⁰

➞ 2x + 3x + 4x = 180⁰

➞ 9x = 180⁰

➞ x = 180⁰/9

➞ x = 20⁰

• 2x = 2(20) = 40⁰
• 3x = 3(20) = 60⁰
• 4x = 4(20) = 80⁰

Hence

• Greatest angle = 80⁰
• Smallest angle = 40⁰

Verification :

➞ 2x + 3x + 4x = 180⁰

➞ 2(20⁰) + 3(20⁰) + 4(20⁰) = 180⁰

➞ 40⁰ + 60⁰ + 80⁰ = 180⁰

➞ 180⁰ = 180⁰

Hence verified