Can a triangle have more than one obtuse angle?
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Can a triangle have more than one obtuse angle?
If we try to draw two obtuse angles and connect them to form a triangle (i.e: only 3 sides), we will see that it is not possible.
Therefore, the answer is no.
No
Look at the angles shown in the figure below.
What is their relationship?
\( \)
An obtuse angle is any angle greater than 90° but less than 180°. Think of it as 'wider' than a right angle (90°).
Because the angles in any triangle must add up to exactly 180°. If you have two obtuse angles (each >90°), their sum alone would exceed 180°, leaving no room for a third positive angle!
Yes! A triangle can have one obtuse angle. The other two angles must be acute (less than 90°) to make the total equal 180°. This is called an obtuse triangle.
The largest obtuse angle approaches 180° but can never reach it. As the obtuse angle gets larger, the other two angles get smaller and approach 0°.
Think of it this way: 180° total budget for all three angles. If you 'spend' more than 90° twice, you've already exceeded your budget before adding the third angle!
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