Chapter 3.5, Problem 20PPS

To determine

To find x so that $m\left|\right|n$ .Identify the postulate or theorem is used.

Answer to Problem 20PPS

  $x={27}^{°}$

Theorem of corresponding angles is used.

Theorem of linear pair is used.

Explanation of Solution

Given information:

Figure

Calculation:

Figure

Here $m\left|\right|n$

From theorem of corresponding angles ${(2x+45)}^o$ is corresponding angle with the linear pair angle of ${(3x)}^o$ .

And sum of linear pair angles is ${180}^o$

Angle ${(2x+45)}^o$ and angle ${(3x)}^o$ are linear pair angles.

Then

  ${(2x+45)}^o+{(3x)}^o={180}^{°}$

On solving

  $5x+45=180$

Subtract 45 both side

  $5x+45-45=180-45$

On solving

  $5x=135$

Divide by 5 both side

  $\frac{5x}{5}=\frac{135}{5}$

On solving

  $x={27}^{°}$