Chapter 3.4, Problem 67SPR

To determine

To find the x and y in the figure.

Answer to Problem 67SPR

  $x=3^{°}$

  $y={\left(\frac{158}{6}\right)}^{°}$

Explanation of Solution

Given information:

Figure

Calculation:

Figure

Lines are parallel

Then $4x^{°}$ and ${(8x-12)}^{°}$ are alternate angles

Then

  $8x-12=4x$

Add 12 both sides

  $8x-12+12=4x+12$

On solving

  $8x=4x+12$

Subtract $4x$ both side

  $8x-4x=4x+12-4x$

On solving

  $4x=12$

Divide by 4 both sides

  $\frac{4x}{4}=\frac{12}{4}$

On solving

  $x=3^{°}$

Vertical opposite angle of ${(6y+10)}^{°}$ is co-interior angle with the ${(8x-12)}^{°}$

And sum of co-interior angles is ${180}^{°}$

Then

  ${(6y+10)}^{°}+{(8x-12)}^{°}={180}^{°}$

Put value of x

  $(6y+10)+(8\times 3-12)=180$

On solving

  $6y+10+12=180$

On solving

  $6y+22=180$

Subtract 22 both sides

  $6y+22-22=180-22$

On solving

  $6y=158$

On divide by 6 both sides

  $y={\left(\frac{158}{6}\right)}^{°}$