If two angles are complementary and one angle is 10 degrees more than the other, what are the measures of the two angles?
Practice Questions
1 question
Q1
If two angles are complementary and one angle is 10 degrees more than the other, what are the measures of the two angles?
40 and 50 degrees
45 and 45 degrees
30 and 60 degrees
35 and 55 degrees
Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: If two angles are complementary and one angle is 10 degrees more than the other, what are the measures of the two angles?
Solution: Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 degrees.
Steps: 9
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 10 degrees more than the other, represent the larger 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: Subtract 10 from both sides: 2x = 80.
Step 7: Divide both sides by 2: x = 40.
Step 8: Find the larger angle by adding 10 to the smaller angle: 40 + 10 = 50.
Step 9: Conclude that the two angles are 40 degrees and 50 degrees.
