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How many obtuse and acute angles can be in a right triangle?
In a right triangle, one of the angles is already given - 90 degrees. Since the angles of a triangle must add up to 180 degrees, the other two must always add up to 90, so that after you add the right angle, the sum is 180. So both of the other angles have to be less than 90. That is, they both must be acute. So there can be NO obtuse angles in a right triangle. There are EXACTLY two acute angles in a right triangle.
If two angles of a triangle are acute then the third must be?
Actually, you cannot conclude anything this way, at least not in regular geometry. For instance, in a "perfect triangle," all 3 angles are acute. In a right triangle, one is a right angle and the other two are acute. It is also possible to have an obtuse angle and two acute angles. The thing is, the 3 angles must add up to 180 degrees.
If a triangle has one acute angle is the triangle necessarily acute?
No, an acute triangle must have all 3 angles under 90 degrees. A triangle can have an acute angle and still be a right triangle or an obtuse triangle.
A triangle with two acute angles must be a right angle?
No. The three angles in a triangle, in plane Euclidean geometry, must add to 180 degrees. Acute angles are less than 90 degrees. Therefore you may have a triangle with three angles which are 60 degrees for instance.
Must a triangle with two acute angles be a right angle?
No. For example, say the two angles are 10° and 20°. Then the other angle is 180°-10°-20°=150° and that is not a right angle. But if the triangle has two equal acute angles of 45 degrees then the 3rd angle must be 90 degrees which will form a right angle triangle.
