If two angles are complementary and one angle is 10 degrees less than the other,

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Question: If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the angles? (2023)

Options:

Correct Answer: 40 degrees and 50 degrees

Exam Year: 2023

Solution:

Let the angles be x and x - 10. Then, x + (x - 10) = 90. Solving gives x = 50 degrees and the other angle is 40 degrees.

If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the angles? (2023)

If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the angles? (2023)

Step 1: Understand that complementary angles add up to 90 degrees.
Step 2: Let the first angle be represented as 'x'.
Step 3: Since one angle is 10 degrees less than the other, represent the second angle as 'x - 10'.
Step 4: Write the equation for the sum of the angles: x + (x - 10) = 90.
Step 5: Simplify the equation: 2x - 10 = 90.
Step 6: Add 10 to both sides of the equation: 2x = 100.
Step 7: Divide both sides by 2 to find x: x = 50 degrees.
Step 8: Calculate the second angle by substituting x back: x - 10 = 50 - 10 = 40 degrees.
Step 9: Conclude that the measures of the angles are 50 degrees and 40 degrees.

Complementary Angles – Complementary angles are two angles whose measures add up to 90 degrees.
Algebraic Representation – Using variables to represent unknown quantities and forming equations based on given relationships.