Chapter SH, Problem 10.3.2EP

To determine

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

  

Answer to Problem 10.3.2EP

The value of $x$ in each triangle is $75$ and as all the angles of the given triangle is below ${90}^{\circ }$ . It is an acute 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,

  $x^{\circ }+{42}^{\circ }+{63}^{\circ }=180$

  $x+105=180$

Now subtracting $105$ from both the sides,

  $x+105-105=180-105$

Solving the above equation,

  $x=75$

Conclusion:

Hence, value of $x$ in each triangle is $75$ and as all the angles of the given triangle is below ${90}^{\circ }$ . It is an acute angle triangle