Chapter 3.5, Problem 19PPS

To determine

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

Answer to Problem 19PPS

  $x={43}^{°}$

Theorem of co-interior angles is used.

Explanation of Solution

Given information:

Figure

Calculation:

Figure

Here $m\left|\right|n$

Then theorem of co-interior angles is used.

And sum of co-interior angle is ${180}^o$

Angle ${(7x-2)}^o$ and angle ${(10-3x)}^o$ are co-interior angles.

Then

  ${(7x-2)}^o+{(10-3x)}^o={180}^{°}$

On solving

  $4x+8=180$

Subtract 8 both side

  $4x+8-8=180-8$

On solving

  $4x=172$

Divide by 4 both side

  $\frac{4x}{4}=\frac{172}{4}$

On solving

  $x={43}^{°}$