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If two angles are complementary and one angle is twice the other, what are the m

Practice Questions

Q1
If two angles are complementary and one angle is twice the other, what are the measures of the angles?
  1. 30 degrees and 60 degrees
  2. 20 degrees and 70 degrees
  3. 45 degrees and 45 degrees
  4. 10 degrees and 80 degrees

Questions & Step-by-Step Solutions

If two angles are complementary and one angle is twice the other, what are the measures of the angles?
  • Step 1: Understand that complementary angles add up to 90 degrees.
  • Step 2: Let the smaller angle be represented as 'x'.
  • Step 3: Since one angle is twice the other, represent the larger angle as '2x'.
  • Step 4: Write the equation for the sum of the angles: x + 2x = 90.
  • Step 5: Combine like terms in the equation: 3x = 90.
  • Step 6: Solve for 'x' by dividing both sides by 3: x = 30 degrees.
  • Step 7: Find the larger angle by calculating 2x: 2x = 2 * 30 = 60 degrees.
  • Step 8: Conclude that the measures of the angles are 30 degrees and 60 degrees.
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