Chapter SH, Problem 10.3.6EP

To determine

The value of $x$ in each triangle and then classify the triangle by its angles and sides.

  

Answer to Problem 10.3.6EP

The value of $x$ in each triangle is ${50}^{\circ }$ and as two angles of triangle are equal it is an Isosceles triangle.

Explanation of Solution

Given:

Triangle with $2$ angles given,

  

Concept Used:

The sum of all the angles of a triangle is ${180}^{\circ }$ .This statement is valid for all types of triangles.

A triangle is called as acute when all the angles are measured less than ${90}^{\circ }$ .

A triangle is called as right angle when the measure of triangle is exact ${90}^{\circ }$ .

A triangle is called as obtuse when measure of angles of triangles is greater than ${90}^{\circ }$ but less than ${180}^{\circ }$ .

Calculation:

As the sum of all the angles of a triangle is ${180}^{\circ }$ ,

To find the value of $x$

The equation is written as,

  $x^{\circ }+{65}^{\circ }+{65}^{\circ }={180}^{\circ }$

  $x+130=180$

Now subtracting $130$ from both the sides,

  $x+130-130=180-130$

Solving the above equation and simplifying,

  $x={50}^{\circ }$

The value of $x$ is ${50}^{\circ }$ .as one of the angle and is obtuse The triangle is an obtuse angled triangle.

Conclusion:

Hence, value of $x$ in each triangle is ${50}^{\circ }$ and as two angles of triangle are equal it is an Isosceles triangle.