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If the angles (5x−2)° and 82° form a pair of supplementary angles, then the value of x is:
20
45
30
90
20
Since supplementary angles sum to 180°, simply subtract 82 from 180 (result 98) and add 2 (result 100), then divide by 5 to get 20.
Two angles, (5x - 2)° and 82°, form a pair of supplementary angles.
(5x−2)+82=180
Since supplementary angles sum to 180°, simply subtract 82 from 180 (result 98) and add 2 (result 100), then divide by 5 to get 20.
Students often confuse 'supplementary' (sum = 180°) with 'complementary' (sum = 90°), leading to incorrect equations.
Define Supplementary Condition
Supplementary angles are two angles that add up to 180 degrees. Therefore, we set the sum of the given expressions to 180.
(5x−2)+82=180
Simplify the Equation
Combine the constant terms: -2 + 82 = 80.
5x+80=180
Solve for x
Subtract 80 from both sides: 5x = 100. Then, divide by 5.
5x=100⟹x=5100=20
A is correct because solving the equation (5x - 2) + 82 = 180 yields 5x = 100, which results in x = 20.
This concept is a foundation for geometry problems involving parallel lines cut by a transversal, where interior angles on the same side are supplementary.
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