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-. The exterior angles obtained on producing the base of a triangleboth ways are 104° and 136º. Find the angles of the triangle. answer this |
Answer» Answer :44° , 60° , 76° Note :★ Linear pairs of angles : Two adjacent angles lying on the same straight LINE is called Linear pair of angles . ★ Sum of linear pair of angles is 180° . ★ Linear pair of angles are SUPPLEMENTARY . ★ Angle sum property of a triangle : The sum of all the INTERIOR angles of a triangle is 180° . Solution :Let's US assume ; • A ∆ABC with base BC . • BC produced along DE . • ∠ABD = 104° and ∠ACE = 136°. Now , => ∠ABD + ∠ABC = 180° { linear pair } => 104° + ∠ABC = 180° => ∠ABC = 180° - 104° => ∠ABC = 76° Also , => ∠ACE + ∠ACB = 180° { linear pair } => 136° + ∠ACB = 180° => ∠ACB = 180° - 136° => ∠ACB = 44° Also , => ∠ABC + ∠ACB + ∠BAC = 180° { angle sum property of ∆ } => 76° + 44° + ∠BAC = 180° => 120° + ∠BAC = 180° => ∠BAC = 180° - 120° => ∠BAC = 60° Hence ,44° , 60° , 76° are the angles of the triangle under CONSIDERATION . |
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