Chapter 11.1, Problem 27IP

To determine

To find: Value of $x,m\angle 4$ and $m\angle 2$

Answer to Problem 27IP

  $\begin{array}{l}m\angle 4={75}^0\\ m\angle 2={75}^0\end{array}$

Value of $x$ is

  $x=5^0$

Explanation of Solution

Given information:

  $\begin{array}{l}m\angle 4=15x^0\\ m\angle 2={\left(11x-20\right)}^0\end{array}$

From the given figure

We can say that $\angle 4$ and $\angle 2$ are corresponding angles

It means both angles are congruent.

  $m\angle 2=m\angle 4$

On substituting values

We get

  $\begin{array}{l}m\angle 2=m\angle 4\\ \Rightarrow 11x+20=15x\\ \Rightarrow 15x-11x=20\\ \Rightarrow 4x=20\\ \Rightarrow x=\frac{20}{4}\\ \Rightarrow x=5\end{array}$

Therefore,

Value of $x$ is $5^0$

We know

  $m\angle 4=15x^0$

On substituting value of $x$

We get

  $\begin{array}{l}m\angle 4=15{\left(5\right)}^0\\ \Rightarrow m\angle 4={75}^0\end{array}$

We know

  $m\angle 2=m\angle 4$

On substituting value of $x$

We get

  $\begin{array}{l}m\angle 2=m\angle 4\\ \Rightarrow m\angle 2={75}^0\end{array}$

Therefore,

  $\begin{array}{l}m\angle 4={75}^0\\ m\angle 2={75}^0\end{array}$