Lines a and b are parallel.
What is the size of angle ?
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Lines a and b are parallel.
What is the size of angle ?
First, let's draw another line parallel to the existing lines that will divide the given angle of 120 degrees in the following way:
Note that the line we drew creates two adjacent and straight angles, each equal to 90 degrees.
Now we can calculate the missing part of the angle known to us using the formula:
Let's write down the known data as follows:
Note that from the drawing we can see that angle alpha and the angle equal to 30 degrees are alternate angles, therefore they are equal to each other.
30
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
The auxiliary line helps us break down the 120° angle into manageable parts. It creates clear angle relationships that we can use with parallel line properties!
Alternate interior angles are on opposite sides of the transversal and inside the parallel lines. They're always equal when lines are parallel.
Look for angles that are in Z-pattern positions (alternate) or F-pattern positions (corresponding). These are equal when lines are parallel.
No! The diagram shows is the smaller angle at the bottom intersection. If it were 60°, the geometry wouldn't match the parallel line relationships.
You can also use co-interior angles (same-side interior). They add up to 180° when lines are parallel, so gives .
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