Q. 54.9( 18 Votes )

# An exterior angle of a triangle is 120° and one of the interior opposite angles is 30°. Find the other angles of the triangle.

Answer :

Given: exterior angle let ∠ ABD = 120°

One interior angle let ∠ BAC = 30°

As we know, using theorem (2) i.e. if a side of the triangle is produced, the exterior angle so formed is equal to the sum of corresponding opposite interior angles.

Hence,

∠ ABD = ∠ BAC + ∠ BCA

**⇒** 120° = 30° + ∠ BCA

⇒ ∠ BCA = 120° - 30°

∠ BCA = x = 90°

As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.

So,

∠BAC + ∠BCA + ∠ ABC = 180°

⇒ 30° + 90° + y = 180°

⇒ y = 180° - 30° - 90°

⇒ y = 60°

Rate this question :

An exterior angle of a triangle is 120° and one of the interior opposite angles is 30°. Find the other angles of the triangle.

Karnataka Board - Mathematics Part IIn an equilateral triangle, each exterior angle is _______

Karnataka Board - Mathematics Part IIn a triangle ABC, ∠B = 50° and ∠A = 60°. Suppose BC is extended to D. Find ∠ACD.

Karnataka Board - Mathematics Part ICompute the value of x in each of the following figures:

Karnataka Board - Mathematics Part I

Sides BC, CA and AB of a triangle ABC are produced in an order, forming exterior angles ∠ACD, ∠BAE, and ∠CBF. Show that ∠ACD + ∠BAE + ∠CBF = 360°.

Karnataka Board - Mathematics Part ISum of the three exterior angles of a triangle is __________

Karnataka Board - Mathematics Part I