You are watching: Why is it impossible for a triangle to contain a 180° angle?
In Geometry, tright here are various feasible angle sizes and each angle drops right into the category of either an acute angle (smaller sized than 90 degrees), a best angle (90 degrees), an obtuse angle (bigger than 90 degrees however smaller than 180 degrees), a right angle (180 degrees), a reflex angle (bigger...
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In Geometry, tright here are various feasible angle sizes and also each angle falls right into the category of either an acute angle (smaller than 90 degrees), a right angle (90 degrees), an obtuse angle (bigger than 90 levels yet smaller sized than 180 degrees), a right angle (180 degrees), a reflex angle (bigger than 180 degrees however smaller than 360 degrees) and a transformation (360 degrees).
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In level or conventional Geomeattempt, the properties of a triangle of any size suppose that a triangle deserve to never before have even more than 180 degrees in between all its angles. It complies with therefore that, in flat Geomeattempt, a triangle cannot have a revolution, which at 360 levels is a full circle roughly a allude. A triangle cannot have a reflex angle either as this is an angle bigger than 180 levels and so the reflex angle would prevent the joining of the three points of a triangle. Do note that a triangle deserve to be formed through the reflex angle on the outside. Picture a triangle. The angle around any type of of the three corners or vertices (i.e. approximately the outside) could be reflex. In such a situation, the angle on the inside could be either acute or obtuse, depending on the triangle.
Two obtuse angles by interpretation mean that tright here would be two angles of (at least) 91 degrees each. 91 + 91 = 182 levels. That is currently too a lot for a triangle, even prior to the 3rd angle has been taken into consideration. Therefore, a triangle can never have even more than one obtusage angle.
When an angle of a triangle is 90 degrees, the triangle cannot have an obtuse angle. The other two must each be less than 90 levels (90 deg + 89 deg + 1 deg = 180 deg). Note that the other two angles have the right to be any type of combicountry however both would be acute angles (smaller sized than 90 degrees).
Therefore, in any kind of triangle where there is at least one obtuse angle (greater than 90 levels however smaller than 180 degrees), it implies that the triangle deserve to just have actually its two other angles smaller sized than 90 levels because an obtuse angle (for instance, 91 degrees) implies tbelow is only 89 levels (at the most) left for the various other two angles. It therefore follows that they should both be much less than 90 degrees and so must both be acute.