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If two angles are complementary and one angle is twice the other, what are the m
If two angles are complementary and one angle is twice the other, what are the measures of the angles?
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Practice Questions
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Q1
If two angles are complementary and one angle is twice the other, what are the measures of the angles?
30 degrees and 60 degrees
20 degrees and 70 degrees
45 degrees and 45 degrees
10 degrees and 80 degrees
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Let the smaller angle be x. Then the larger angle is 2x. The equation x + 2x = 90 gives x = 30 degrees and 2x = 60 degrees.
Questions & Step-by-step Solutions
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Q
Q: If two angles are complementary and one angle is twice the other, what are the measures of the angles?
Solution:
Let the smaller angle be x. Then the larger angle is 2x. The equation x + 2x = 90 gives x = 30 degrees and 2x = 60 degrees.
Steps: 8
Show Steps
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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