Chapter 1.1, Problem 18E

To determine

To determine the value of x .

Answer to Problem 18E

  $x={85}^{\circ }$

Explanation of Solution

Given:

  

Concept used:

The sum of interior angles of a quadrilateral is ${360}^{\circ }$ .

Calculation:

We have,

  

From the above figure, the following equation can be written.

  $\Rightarrow x^{\circ }+{150}^{\circ }+{77}^{\circ }+{48}^{\circ }={360}^{\circ }$

  $\Rightarrow x^{\circ }+{275}^{\circ }={360}^{\circ }$

  $\Rightarrow x^{\circ }+{275}^{\circ }-{275}^{\circ }={360}^{\circ }-{275}^{\circ }$ (Subtracting ${275}^{\circ }$ from both sides)

  $\Rightarrow x^{\circ }={85}^{\circ }$

Conclusion:

Hence, the required value of x is ${85}^{\circ }.$