Question

Name the types of following triangles: $$\mathrm{\Delta }LMN$$ with $$m\mathrm{\angle }L={30}^{\circ };m\mathrm{\angle }M={70}^{\circ };$$ and $$m\mathrm{\angle }N={80}^{\circ }$$.

Answer 1

Hint: Here, we have to find the type of triangle with the given measures of angle. We will use the classification of the triangle based on the angle of the triangle. We will then compare the given measures of triangles with the different types of triangles and find the required answer. A triangle is a polygon with three sides. An angle is defined as the figure formed where two line segments meet at a point.

Complete step-by-step answer:
We will first draw the diagram based on the given information.
     

We know that the triangles are classified on the basis of angles of a triangle. If all the angles of the triangle are less than $${90}^{\circ }$$, then the triangle is known as an acute angle triangle.
If only one of the angles of a triangle is a right angle, then the triangle is known as a right angled triangle.
If only one of the angles of a triangle is greater than $${90}^{\circ }$$, then the triangle is known as an obtuse angle triangle.
Now, let $$\mathrm{\Delta }LMN$$ be a triangle.
We are given that $$\mathrm{\angle }L={30}^{\circ }$$,$$\mathrm{\angle }M={70}^{\circ }$$ and $$\mathrm{\angle }N={80}^{\circ }$$.
We know that the sum of the angles of a triangle is $${180}^{\circ }$$.
Since all the angles of a triangle measures less than $${90}^{\circ }$$, $$\mathrm{\angle }L,\mathrm{\angle }M,\mathrm{\angle }N<{90}^{\circ }$$
Thus the given triangle is an acute angle triangle.

Note: Triangles are classified into three types based on the sides of the triangle. They are equilateral triangles, isosceles triangles, and scalene triangles.
If all the three sides of a triangle are equal in length, then the triangle is known as an equilateral triangle.
If two sides of a triangle are equal in length and the third side of a triangle is different, then the triangle is known as Isosceles triangle.
If all the three sides of a triangle are different in length, then the triangle is known as a scalene triangle.