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You are watching: Can a triangle have two obtuse angles


In Geometry, there space various possible angle sizes and also each angle falls into the category of one of two people an acute angle (smaller 보다 90 degrees), a best angle (90 degrees), one obtuse angle (bigger than 90 degrees yet smaller 보다 180 degrees), a directly angle (180 degrees), a reflex angle (bigger...

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In Geometry, there are various feasible angle sizes and also each angle falls into the classification of either an acute edge (smaller than 90 degrees), a right angle (90 degrees), an obtuse angle (bigger 보다 90 degrees however smaller than 180 degrees), a right angle (180 degrees), a reflex edge (bigger 보다 180 degrees however smaller 보다 360 degrees) and also a transformation (360 degrees).

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In level or timeless Geometry, the nature of a triangle of any size median that a triangle can never have an ext than 180 degrees in between all its angles. It follows because of this that, in flat Geometry, a triangle cannot have a revolution, which at 360 levels is a complete circle roughly a point. A triangle cannot have actually a reflex angle either together this is an edge bigger 보다 180 degrees and also so the reflex edge would prevent the involvement of the three points of a triangle. Do keep in mind that a triangle can be developed with the reflex angle on the outside. Snapshot a triangle. The edge around any kind of of the three corners or vertices (i.e. Around the outside) could be reflex. In such a case, the edge on the inside might be either acute or obtuse, depending upon the triangle. 

Two obtuse angle by meaning mean the there would certainly be two angles the (at least) 91 levels each. 91 + 91 = 182 degrees. The is currently too lot for a triangle, even prior to the third angle has actually been considered. Therefore, a triangle can never have an ext than one obtuse angle.

When an edge of a triangle is 90 degrees, the triangle cannot have an obtuse angle. The other two need to each be less than 90 levels (90 deg + 89 deg + 1 deg = 180 deg). Keep in mind that the other two angles have the right to be any mix but both would be acute angles (smaller 보다 90 degrees). 

Therefore, in any triangle whereby there is at least one obtuse angle (greater 보다 90 degrees yet smaller than 180 degrees), it way that the triangle can only have its two various other angles smaller than 90 degrees because an obtuse edge (for example, 91 degrees) way there is only 89 degrees (at the most) left because that the other two angles. It therefore follows the they must both be less than 90 degrees and also so should both it is in acute.