The exterior angles, obtained on producing the base of a triangle both ways are 104° and 136°. Find all the angles of the triangle.
Question:
The exterior angles, obtained on producing the base of a triangle both ways are 104° and 136°. Find all the angles of the triangle.
Solution:
∠ACD = ∠ABC + ∠BAC [Exterior angle property]
Now ∠ABC = 180° − 136° = 44° [Linera pair]
∠ACB = 180° − 104° = 76° [Linera pair]
Now, In ΔABC
∠A + ∠ABC + ∠ACB = 180° [Sum of all angles of a triangle]
⇒ ∠A + 44° + 76° = 180°
⇒ ∠A = 180° − 44° − 76°
⇒ ∠A = 60°
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