Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)
Practice Questions
1 question
Q1
Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)
30 degrees
60 degrees
90 degrees
120 degrees
If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.
Questions & Step-by-step Solutions
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Q
Q: Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)
Solution: If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.
Steps: 7
Step 1: Understand that two lines are perpendicular if they meet at a right angle (90 degrees).
Step 2: Know that the angles made by two perpendicular lines add up to 90 degrees.
Step 3: Identify the angle of the first line with the horizontal, which is given as 30 degrees.
Step 4: Use the formula for perpendicular lines: Angle of first line + Angle of second line = 90 degrees.
Step 5: Substitute the known angle into the formula: 30 degrees + Angle of second line = 90 degrees.
Step 6: Solve for the angle of the second line: Angle of second line = 90 degrees - 30 degrees.
Step 7: Calculate the result: Angle of second line = 60 degrees.
