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You are watching: A triangle cannot have more than one right angle

In Geometry, there are various possible angle sizes and also each angle drops into the category of one of two people an acute edge (smaller 보다 90 degrees), a ideal angle (90 degrees), one obtuse angle (bigger 보다 90 degrees however smaller 보다 180 degrees), a straight angle (180 degrees), a reflex angle (bigger...

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In Geometry, there space various possible angle sizes and each angle falls into the classification of either an acute edge (smaller than 90 degrees), a best angle (90 degrees), an obtuse angle (bigger than 90 degrees however smaller than 180 degrees), a straight angle (180 degrees), a reflex angle (bigger 보다 180 degrees but smaller 보다 360 degrees) and a revolution (360 degrees).

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In flat or traditional Geometry, the properties of a triangle of any kind of size median that a triangle deserve to never have much more than 180 degrees in between all its angles. It follows as such that, in flat Geometry, a triangle cannot have a revolution, which in ~ 360 levels is a full circle around a point. A triangle cannot have a reflex angle either together this is an angle bigger than 180 degrees and also so the reflex angle would avoid the involvement of the three points that a triangle. Do keep in mind that a triangle can be formed with the reflex angle on the outside. Snapshot a triangle. The edge around any kind of of the 3 corners or vertices (i.e. About the outside) might be reflex. In such a case, the edge on the inside can be one of two people acute or obtuse, depending upon the triangle.

Two obtuse angles by meaning mean that there would certainly be 2 angles that (at least) 91 levels each. 91 + 91 = 182 degrees. The is currently too much for a triangle, even before the third angle has been considered. Therefore, a triangle can never have an ext than one obtuse angle.

When an angle of a triangle is 90 degrees, the triangle cannot have actually an obtuse angle. The various other two have to each be less than 90 degrees (90 deg + 89 deg + 1 deg = 180 deg). Note that the various other two angles can be any combination but both would be acute angles (smaller 보다 90 degrees).

Therefore, in any type of triangle whereby there is at the very least one obtuse edge (greater than 90 degrees yet smaller 보다 180 degrees), it method that the triangle can only have its two various other angles smaller sized than 90 degrees since an obtuse angle (for example, 91 degrees) way there is only 89 levels (at the most) left for the other two angles. It because of this follows the they need to both be much less than 90 degrees and also so need to both be acute.