Question

One of the interior angles of a triangle is equal to 30, and one of the exterior angles is equal to 40. Find the remaining interior angles of this triangle

Answer 1

............... ......

Answer 2

Answer:

10° and 140°

Step-by-step explanation:

In a triangle,

The sum of any two interior angles is equal to the opposite exterior angle,

Let the angles of a triangle are x, y and z,

Such that,

x = 30°,

By the above statement,

x + y = exterior angle at Z,

If the exterior angle at Z = 40°,

30° + y = 40° ⇒ y = 10°,

Also, the sum of all interior angles of a triangle is equal to 180°,

⇒ x + y + z = 180°

⇒ 30 + 10 + z = 180°

⇒ 40 + z = 180°

⇒ z = 140°,

Hence, the remaining interior angles of this triangle are 10° and 140°