Chapter SH, Problem 10.3.4EP

To determine

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

  

Answer to Problem 10.3.4EP

The value of $x$ in each triangle is ${45}^{\circ }$ .As one of the angle of triangle is above ${90}^{\circ }$ . It is an obtuse angle 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,

  $\begin{array}{l}{x}^{\circ }+{40}^{\circ }+{95}^{\circ }={180}^{\circ }\\ x+135=180\end{array}$

Now subtracting $135$ from both the sides,

  $x+135-135=180-135$

Solving the above equation and simplifying,

  $x={45}^{\circ }$

.Conclusion:

Hence, value of $x$ in each triangle is ${45}^{\circ }$ .As one of the angle of triangle is above ${90}^{\circ }$ . It is an obtuse angle triangle.