Question

10 One angle of a triangle is equal to the sum of the other two. If the ratio of the other two
angles is 7:8, find the angles of the triangle..​

Answer 1

Answer :

• Angles of triangle are 42⁰ , 48⁰ and 90⁰

Given :

• One angle of a triangle is equal to the sum of the other two
• The ratio of the other two angles is 7 : 8

To find :

• Angles of the triangle

Solution :

Given the ratio of the other two angles is 7 : 8 so ,

• Let the first triangle be 7x
• Let the second triangle be 8x

According to question, Given that, One angle of a triangle is equal to the sum of the other two so,

• Let the third angle be 7x + 8x

We know that

• Sum of all angles in a triangle is equal to 180⁰

According to question,

➝ 7x + 8x + 7x + 8x = 180⁰

➝ 14x + 16x = 180⁰

➝ 30x = 180⁰

➝ x = 180/30

➝ x = 6

Finding the angles of a triangle :

➝ 7x = 7(6) = 42⁰

➝ 8x = 8(6) = 48⁰

➝ 7x + 8x = 7(6) + 8(6) = 42 + 48 = 90⁰

Hence , Angles of triangle are 42⁰ , 48⁰ and 90⁰