Chapter 11.1, Problem 29PPS

a.

To determine

To write: An equation to find the value of x. Also find the value of x.

Answer to Problem 29PPS

The equation is $2x^{\circ }+6x^{\circ }={180}^{\circ }$ and the value of x is ${22.5}^{\circ }$

Explanation of Solution

Given information:

Given figure is,

  

Consider the figure as,

  

From the figure it is clear that,

  $2x^{\circ }+6x^{\circ }={180}^{\circ }$

On solving,

  $\begin{array}{c}2x^{\circ }+6x^{\circ }={180}^{\circ }\\ 8x^{\circ }={180}^{\circ }\\ x=\frac{180}{8}\\ x={22.5}^{\circ }\end{array}$

Therefore, the equation is $2x^{\circ }+6x^{\circ }={180}^{\circ }$ and the value of x is ${22.5}^{\circ }$

b.

To determine

To find: The values of the angles.

Answer to Problem 29PPS

The values of the angles are ${45}^{\circ }\text{ and }{135}^{\circ }$ .

Explanation of Solution

Given information:

Diagram is given as,

  

Also, $x={22.5}^{\circ }$

Consider the diagram as,

  

Also given value of x is $x={22.5}^{\circ }$

Then, $2x=2\times {22.5}^{\circ }={45}^{\circ }$ and $6x=6\times {22.5}^{\circ }={135}^{\circ }$

Therefore, the values of the angles are ${45}^{\circ }\text{ and }{135}^{\circ }$ .