Question

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in the figure, ( a parallel b ). what is the value of ( x )?

example 3
use algebra to find unknown angles
in the figure, ( a ), ( b ), and ( c ) are parallel lines. what is the value of ( x )?
write an equation that relates the angle measures and solve.
( (x + 25) + 75 = 180 )
( x + 100 = 180 )
( x + 100 - 100 = 180 - 100 )
( x = 80 )

look for relationships
what is another way to use the angle relationships to find the value of ( x )?

the angle that measures ( (x + 25)^circ ) is supplementary to the angle that measures ( 75^circ )

( angle 10 ) and the ( 75^circ ) angle are corresponding angles...

Explanation:

Step1: Identify supplementary angles

The angle labeled \(x^\circ\) and the \(125^\circ\) angle (vertical angle of the angle adjacent to \(x\)) are supplementary (they form a linear pair, so their sum is \(180^\circ\)).

Step2: Set up the equation

$$x + 125 = 180$$

Step3: Solve for x

$$x = 180 - 125$$

Answer:

\(x = 55\)

Alternative Method (using alternate interior angles):

Step1: Identify alternate interior angles

The angle supplementary to \(x\) is equal to \(125^\circ\) (alternate interior angles with the given \(125^\circ\) angle).

Step2: Set up supplementary equation

$$x + 125 = 180$$

Step3: Calculate x

$$x = 180 - 125$$