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°
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