Chapter 11.1, Problem 3GP

To determine

To classify the pair of angles shown in the picture and then find the value of x.

Answer to Problem 3GP

The angles are supplementary angles and value of $x^{\circ }={75}^{\circ }$ .

Explanation of Solution

Given:

  

Calculation:

The two angles combined to give straight angle. So, the angles are supplementary angles.

Now, the sum of the two angles is ${180}^{\circ }$ .

So,

  $\begin{array}{c}{x}^{\circ }+{105}^{\circ }={180}^{\circ }\\ x^{\circ }={180}^{\circ }-{105}^{\circ }\\ x^{\circ }={75}^{\circ }\end{array}$

Conclusion:

The angles are supplementary angles and value of $x^{\circ }={75}^{\circ }$ .