Question

The diagram shows parallel lines cut transversal. what is the measure of ∠4?

Answer 1

Let us solve for x first

Corresponding angles are equal.

Therefore,

$\begin{gathered} 7x+75=2x+100 \\ 7x-2x=100-75 \\ 5x=25 \\ x=\frac{25}{5}=5 \end{gathered}$

The measure of ∠4 is

$\begin{gathered} \angle4+7x+75=180^0\text{ \lparen Sum of the angles on a straight line is }180^0) \\ \angle4+7(5)+75=180^0 \\ \angle4+35+75=180^0 \\ \angle4+110^0=180^0 \\ \angle4=180^0-110^0=70^0 \\ \therefore\angle4=70^0 \end{gathered}$

Hence,

$\begin{equation*} \angle4=70^0 \end{equation*}$