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If two parallel lines are cut by a transversal, and one pair of the corresponding angles formed are (x+30)° and (2x−10)°, then find the value of x.
30
40
50
60
60
Since corresponding angles of parallel lines are equal, simply equate the two expressions: x+30=2x−10. Subtracting x from both sides gives 30=x−10, so x=40.
Two parallel lines cut by a transversal where corresponding angles are (x + 30)° and (2x - 10)°.
(x+30)=(2x−10)
Since corresponding angles of parallel lines are equal, simply equate the two expressions: x+30=2x−10. Subtracting x from both sides gives 30=x−10, so x=40.
Students often confuse corresponding angles with supplementary angles. Corresponding angles are strictly equal when the lines are parallel.
Identify Relationship
When two parallel lines are intersected by a transversal, the corresponding angles are equal.
(x+30)°=(2x−10)°
Solve for x
Isolate the variable x by rearranging the terms: 30+10=2x−x.
x=40
Verification
Substitute x=40 into the expressions: (40+30)=70° and (2×40−10)=80−10=70°. Since both are 70°, the value is correct.
70°=70°
D is correct because solving the equation x+30=2x−10 yields x=40.
This concept of equal angles is fundamental to solving problems in geometry involving alternate interior and exterior angles as well.
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