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The difference in the measures of two complementary angles is 18°. Find the measure of the smaller angle.
36°
38°
35°
36°
36°
For two numbers with sum S and difference D, the smaller number is (S−D)/2. Here, (90−18)/2=72/2=36°.
Two angles are complementary, meaning their sum is 90°. The difference between their measures is 18°.
x+y=90, x−y=18
For two numbers with sum S and difference D, the smaller number is (S−D)/2. Here, (90−18)/2=72/2=36°.
Confusing complementary angles (sum = 90°) with supplementary angles (sum = 180°).
Define the system of equations
Let the two complementary angles be x and y (where x>y). Since they are complementary, their sum is 90°. Given their difference is 18°:
x+y=90x−y=18
Solve for the smaller angle
Subtract the two equations to isolate y: (x+y)−(x−y)=90−18, which simplifies to 2y=72. Divide by 2 to find y.
2y=72⇒y=36°
Verify results
If y=36°, then x=90°−36°=54°. The difference 54°−36°=18°, which matches the given condition.
54°−36°=18°
A is correct because the smaller angle is calculated as 36°.
Always remember that 'Complementary' implies 90° sum (think 'C' for 'Corner' or 90°) and 'Supplementary' implies 180° sum (think 'S' for 'Straight line').
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