Chapter 11.8, Problem 35CCR

a.

To determine

To find: The value of $x$ .

Answer to Problem 35CCR

Value of $x$ is $2^0$

Explanation of Solution

Given information:

Angle $ABC=7x^0$

Angle $DBE={\left(3x+8\right)}^0$

Given

Angle $ABC=7x^0$

Angle $DBE={\left(3x+8\right)}^0$

We know vertical angles are equal.

Using that

We get

Angle $ABC=$ Angle $DBE$

  $\begin{array}{l}\Rightarrow 7x=3x+8\\ \Rightarrow 7x-3x=8\\ \Rightarrow 4x=8\\ \Rightarrow \frac{4x}{4}=\frac{8}{4}\\ \Rightarrow x=2^0\end{array}$

Therefore,

Value of $x$ is $2^0$

b.

To determine

To find: Angle $DBE$ .

Answer to Problem 35CCR

Angle $DBE={14}^0$

Explanation of Solution

Given information:

Angle $ABC=7x^0$

Angle $DBE={\left(3x+8\right)}^0$

Given

Angle $ABC=7x^0$

Angle $DBE={\left(3x+8\right)}^0$

We know vertical angles are equal.

Using that

We get

Angle $ABC=$ Angle $DBE$

  $\begin{array}{l}\Rightarrow 7x=3x+8\\ \Rightarrow 7x-3x=8\\ \Rightarrow 4x=8\\ \Rightarrow \frac{4x}{4}=\frac{8}{4}\\ \Rightarrow x=2^0\end{array}$

We know

Angle $DBE=3x+8$

On substituting value of $x$

We get

  $\Rightarrow$ Angle $DBE=3\left(2\right)+8$

  $\Rightarrow$ Angle $DBE=6+8$

  $\Rightarrow$ Angle $DBE={14}^0$

Therefore,

Angle $DBE={14}^0$