Question

How many acute angles does a scalene triangle have?

Answer 1

Hint:
Here we are given a scalene triangle and we are asked the number of the acute angles it can have. So while approaching this question first of all we should know about the scalene triangle and the acute angles. So the acute angles are the angles whose measure is less than the \[{90^ \circ }\] and the scalene triangles are those types of the triangles whose all the sides have different measure and all the angles are of different measure also. Using their definition we can carry out the conclusion about the number of acute angles the scalene triangle can have in the complete step by step solution.

Complete step by step solution:
Here in this question we are given a scalene triangle and we are asked the number of the acute angles it can have which can be determined as looking on their basic definitions that is a scalene triangle is the type of the triangles whose all the sides have different measure and the all the angles are of different measure also and the acute angles are the angles whose measure is less than \[{90^ \circ }\]. Now using this we would find the number of the acute angles a scalene triangles can have-
As the total sum of all the angles of the triangle is \[{180^0}\] and the measure of the acute angles is less than \[{90^ \circ }\] so a scalene triangle can have \[2\] or \[3\] acute angles
So the scalene triangle can have \[2\] or \[3\] acute angles.

Note:
While approaching such kind of the question one should know about the different types of the angles that are acute (whose measure is less than the \[{90^ \circ }\]), right angles whose measure is equal to the \[{90^ \circ }\]) and obtuse angles (whose measure is more than the \[{90^ \circ }\]) and the different types of the triangles that are scalene(whose none of the sides are equal), equilateral(whose all three sides are equal and the each angle is of the \[{60^ \circ }\]), isosceles(whose two sides and angles are equal in the measure) and the right angled triangle (whose one angle of the triangles is equal to the \[{90^ \circ }\]).