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Example 1: Identify the corresponding angles in the figure which shows two parallel lines 'm' and 'n' cut by a transversal 't'.
Solution: In the given figure, two parallel lines are cut by a transversal, and the corresponding angles in the figure are ∠1 and ∠3; and ∠2 and ∠5.
Example 2: Find the value of x in the given parallel lines 'a' and 'b', cut by a transversal 't'
Solution: The given parallel lines are cut by a transversal, therefore, the marked angles in the figure are the alternate interior angles which are equal in measure. This means, 8x - 4 = 60°, and 8x = 64, x = 8.
Therefore, the value of x = 8.
Example 3: Lines a and b are cut by a transversal c and m<1 is 60°. Assume that line a is parallel to line b. Find the measures of all the other angles.
Solution: There are many angle pair relationships that you can use to obtain the measures of the different angles. Here is one way of doing it.
m<2 = 120° since <1 and <2 are supplementary angles
m<3 = 120° since <2 and <3 are vertical angles
m<4 =60° since <1 and <4 are vertical angles
m<5 =60° since <1 and <5 are corresponding angles
m<6 = 120° since <2 and <6 are corresponding angles
m<7 = 120° since <3 and <7 are corresponding angles
m<8 = 60° since <4 and <8 are corresponding angles
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