Question

example 3 - using properties of parallel lines
find the value of x.
solution
by the consecutive interior angles theorem, the two given angles are
supplementary.
\\( \frac { 2 } { 3 } ( x + 27 ) + ( 3 x - 25 ) = 180 \\)
consecutive interior angles theorem
\\( 2 ( x + 27 ) + 3 ( 3 x - 25 ) = 540 \\)
multiplication property of equality
\\( 2 x + 54 + 9 x - 75 = 540 \\)
distributive property
\\( 11 x - 21 = 540 \\)
simplify.
\\( 11 x = 561 \\)
addition property of equality
\\( x = 51 \\)
division property of equality
so, the value of x = 51.
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try this video for extra example 2 and 3 - using properties of parallel lines

1. find the value of x.
2. find the value of x.

Explanation:

Step1: Find the angle adjacent to \(120^{\circ}\)

The adjacent angle to \(120^{\circ}\) is \(180 - 120=60^{\circ}\) (supplementary angles).

Step2: Set up the equation for \(x\)

Since \(2x\) and the \(60^{\circ}\) angle are corresponding angles (parallel lines \(a\) and \(b\)), \(2x = 60\)

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{60}{2}=30\)

Answer:

\(x = 30\)