Question
A student when asked to measure two exterior angles of $\triangle \text{ABC}$ observed that the exterior angles at A and B are of 103° and 74° respectively. Is this possible? Why or why not?
✓
Answer
Internal angle at A + External angle at A = 180º
Internal angle at A + 103º =180º
Internal angle at A = 77°
Internal angle at B + External angle at B = 180º
Internal angle at B + 74º = 180º
Internal angle at B = 106º
Sum of internal angles at A and B = 77° + 106º
= 183°
It means that the sum of internal angles at A and B is greater than 180°, which cannot be possible.
Internal angle at A + 103º =180º
Internal angle at A = 77°
Internal angle at B + External angle at B = 180º
Internal angle at B + 74º = 180º
Internal angle at B = 106º
Sum of internal angles at A and B = 77° + 106º
= 183°
It means that the sum of internal angles at A and B is greater than 180°, which cannot be possible.
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