Question

use the image below to answer solve the problems.
find the ( m angle 4 ) given that ( a | b )
( m angle 4=-2 x+116 )
( m angle 5=8 x-80 )
9.
( 112^{circ} )
( 68^{circ} )
( 24^{circ} )
( 156^{circ} )
clear all

Explanation:

Step1: Use the property of alternate interior angles

Since \(a\parallel b\), \(\angle4\) and \(\angle5\) are alternate interior angles. So \(m\angle4 = m\angle5\).
\(-2x + 116=8x - 80\)

Step2: Solve the equation for \(x\)

Add \(2x\) to both sides: \(116 = 10x-80\)
Add \(80\) to both sides: \(196 = 10x\)
Divide both sides by \(10\): \(x = 19.6\)

Step3: Calculate \(m\angle4\)

Substitute \(x = 19.6\) into \(m\angle4=-2x + 116\)
\(m\angle4=-2\times19.6+116\)
\(m\angle4=-39.2 + 116\)
\(m\angle4 = 76.8\) (Wait, this is wrong. Let's check the property again. Actually, \(\angle4\) and \(\angle5\) are same - side interior angles. So \(m\angle4+m\angle5 = 180^{\circ}\))
\(-2x + 116+8x - 80=180\)
\(6x+36 = 180\)
\(6x=144\)
\(x = 24\)
Substitute \(x = 24\) into \(m\angle4=-2x + 116\)
\(m\angle4=-2\times24 + 116\)
\(m\angle4=-48+116\)
\(m\angle4 = 68^{\circ}\)

Answer:

\(68^{\circ}\)