Question

sally states that a triangle can only have one obtuse or right angle however a triangle must have at least to acute angles is sally correct explain

Answer 1

Yes Sally is correct

Explanation:

We note that an obtuse angle = Angle larger than 90°

Acute angle = Angle lesser than 90°

Sum of angles in a triangle = 180°

Number of angles in triangle = 3

Therefore, assuming the angles in the triangle are A, B and C where C is obtuse or at least 90°, then we have;

C ≥ 90° therefore taken as obtuse

A + B + C = 180°

A + B = 180° - C

∴ A + B = 180°- (≥90°) = ≤90°

Hence A + B ≤ 90°

Which means A and B are less than 90°, therefore both acute

Therefore, a triangle can have only one angle (C in the above example) greater than or equal to 90° and at least two acute angles A and B in the above example.

Answer 2

Answer: Yes, Sally is correct.

Step-by-step explanation: Both of Sally's statements are mathematically correct, because to begin with the total of the sum of angles in a triangle is always equal to 180 degrees. An acute angle is less than 90 degrees and that means we can calculate three acute angles from a triangle.

Also an obtuse angle is greater than 90 degrees, but less than 180 degrees. That means, a triangle cannot have more than one obtuse angle. If for instance a triangle has an angle measuring 91 degrees (obtuse angle), then the other two angles will be divided between the remainder which is 89 degrees.

Also a triangle can only have one right angle (which measures 90 degrees). This implies that, in a right angled triangle, there cannot be another 90 degree angle, because that would reduce the shape to two angles only (which is not possible).

A triangle can contain at least two acute angles (and at most three acute angles) and all three angles in either case must add up to 180 degrees.

Please refer to the picture attached for more information.