Question

current skill
find the measure of angle 4.

Explanation:

Step1: Use the property of same - side interior angles

Since the two lines are parallel, \(2x + 143\) and \(-9x-33\) are same - side interior angles. So \(2x + 143+(-9x - 33)=180\).

$$\begin{align*} 2x+143 - 9x-33&=180\\ -7x+110&=180\\ -7x&=180 - 110\\ -7x&=70\\ x&=- 10 \end{align*}$$

Step2: Find the measure of \(2x + 143\)

Substitute \(x =-10\) into \(2x + 143\), we get \(2\times(-10)+143=-20 + 143 = 123\).

Step3: Use the property of adjacent angles

Since \(\angle4\) and \(2x + 143\) are adjacent angles and form a linear pair. But if we consider the relationship between angles, \(\angle4\) and \(2x + 143\) are vertical angles. So \(\angle4=123\)

Answer:

\(123\)