How Many Right Angles Can a Triangle Have

Introduction

A polygon is a geometric structure with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges. Vertex or corners refer to the intersection of two line segments, where an angle is created. The number of angles of a polygon corresponds to the number of its sides. Every polygon is classified based on the number of sides it consists of and the angles its sides make with their adjacent sides. An example is a heptagon consisting of seven sides or a square, a quadrilateral with four sides with equal lengths of sides and equal degrees of angles.

Triangle

Triangles are area-enclosed geometrical shapes or polygons made up of three connected line segments. A triangle's three sides formed by the segments create three distinct angles by the adjoining sides. Its angles do not always measure the same, unlike some of the other geometric shapes like squares and rectangles. The sum of all three angles of a triangle is always 180° and it is never less or more than it in any possible situation. The sides and angles of a triangle always correspond to each other, so if a triangle has 2 equal sides, it’ll always have 2 equal angles as well that will be opposite to the equal sides. The angle opposite to the longest side will be the greatest angle or the angle with the highest degree. For example, A triangle with two equal angles and two equal sides is called an isosceles triangle.

Right Angle

When two segments meet at such a point that they form a perpendicular or an ‘L’ letter-like shape, the measure of the angle formed by them is 90°. An angle formed at 90° is called a right angle. In quadrilaterals like squares and rectangles whose sum of angles equals 360°, each of the measures of the angles is 90° thus making four right angles in squares and rectangles. An angle in its simplest can be measured manually by geometrical equipment called a protractor.

Right-Angled Triangle

A right-angled triangle is one in which one of the angles is 90°, and the total of the other two angles is 90°. The 90° sides are regarded as perpendicular and the base. The hypotenuse is the side that lies directly across from the 90° angle. The longest side in a right-angled triangle is called the hypotenuse. The right-angle triangle's last two interior angles add up to 90°. Half of the product of the neighbouring sides of the right angle makes up the area of the right-angle triangle.

How Many Right Angles Can a Triangle Have?

Since\\ the\ sum\ of\ all\ the\ three\ angles\ should\ be\ 180\degree,\\

\\Let\ the\ three\ angles\ be\ \angle {A}, \angle {B}\ and\ \angle {C}\\

\\\therefore\ \angle {A}+ \angle {B}+ \angle {C}= 180\degree\\

\\\text {now, if one of the angles, say} \angle {A}=90\degree,\\

then\\

90\degree+ \angle {B}+ \angle {C}= 180\degree\\

so,\ \angle {B}+ \angle C= 180-90=90\degree\\

\\\text {this is possible as explained above in case of a right-angled triangle}\\

\text {but if more than one angle is taken as right angles, say} \angle {A}= \angle {B}= 90\degree\\

\\then, 90\degree+ 90\degree+ \angle C= 180\degree\\

\text {In which case,} \angle {C}=O,\ \text {which is practically impossible}\\

\\\therefore\ \text {A triangle can only have one right angle.}\\