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In the given figure, the side BC of a Δ ABC is produced on both sides. Then ∠ 1 + ∠ 2 is equal to :
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- ∠A + 180°
- 180° − ∠A
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1 (∠A + 180°) 2 - ∠A + 90°
- None of these
Correct Option: A
From the given figure, In ΔABC
We know that , Exterior angle = Sum of two interior angles
∠1 = ∠A + ∠5 ................. ( 1 )
and ∠2 = ∠A + ∠6 ................. ( 2 )
Adding equations ( 1 ) and ( 2 ).
∠1 + ∠2 = 2∠A + ∠5 + ∠6
= 2∠A + (180° − ∠A) = ∠A + 180°
The given question can be restated as the sum of two exterior angles exceeds ∠A of the ΔABC by 2 right angles.
