Question

one of the exterior angles of a triangle is 110 and the interior opposite angles are in the ratio of 5:6. find all the angles of triangle.
​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Let the given angles be 5x and 6x respectively.

So,

5x + 6x = 110° (exterior angle property)

11x = 110

x = 10

5x = 50°

6x = 60°

Let the other angle be y. So,

y + 110 = 180 (angle sum property)

y = 70°

All angles => 50°, 60°, 70°.

HOPE IT HELPS!!!

Answer 2

ᴀɴsᴡᴇʀ

★ given →

• exterior angle of a triangle is 110° and ratio of two opposite interior angles is 5:6

★ to find →

• find all the angles of triangle?

★ solution →

we have, ratio of two opposite interior angles of a triangle is 5:6

let two opposite interior angles of a triangle be 5x and 6x

☆ exterior angle property of a triangle : exterior angle of a triangle is equal to sum of two opposite interior angles of a triangle

➪ 110 = 5x + 6x

➪ 110 = 11x

➪ 11x = 110

➪ x = 110/11

➪ x = 10

so, x = 10 is common multiple of angles

therefore two interior angles of the triangle is

• 5 × 10 = 50°
• 6 × 10 = 60°

now we have to find third angle of the triangle;

☆ angle sum property of a triangle : sum of all angles of a triangle is 180°

➪ sum of all angles = 180°

let third angle be y

➪ 50° + 60° + y = 180°

➪ 110° + y = 180°

➪ y = 180° - 110°

➪ y = 70°

so, third angle of the triangle is 70°

therefore, angles of the triangle are;

• 50°
• 60°
• 70°