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l and m are two lines perpendicular to each other. What is the measure of the angle between them?
- a)10∘
- b)50∘
- c)40∘
- d)90∘
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
l and m are two lines perpendicular to each other. What is the measure...
The angle between perpendicular lines is 90°.
Most Upvoted Answer
l and m are two lines perpendicular to each other. What is the measure...
Explanation:
When two lines are perpendicular to each other, they form a right angle. A right angle measures 90 degrees. Therefore, the measure of the angle between the two lines is 90 degrees.
Proof:
To prove that the angle between two perpendicular lines is 90 degrees, we can use the concept of alternate angles and the fact that the sum of angles in a straight line is 180 degrees.
1. Let's assume that line L is perpendicular to line M.
2. We can draw a transversal line that intersects both L and M.
3. When a transversal intersects two lines, it creates a pair of alternate angles.
4. Since L and M are perpendicular, the alternate angles created by the transversal will be congruent (equal in measure).
5. Let's label the alternate angles as angle 1 and angle 2.
6. Now, let's consider the straight line formed by line L, the transversal, and line M.
7. The sum of angles in a straight line is 180 degrees.
8. Therefore, angle 1 + angle 2 = 180 degrees.
9. Since angle 1 and angle 2 are congruent, we can rewrite the equation as 2 * angle 1 = 180 degrees.
10. Solving for angle 1, we get angle 1 = 90 degrees.
11. Hence, the measure of the angle between the perpendicular lines L and M is 90 degrees.
Conclusion:
The measure of the angle between two lines perpendicular to each other is always 90 degrees. Therefore, the correct answer is option D) 90.
When two lines are perpendicular to each other, they form a right angle. A right angle measures 90 degrees. Therefore, the measure of the angle between the two lines is 90 degrees.
Proof:
To prove that the angle between two perpendicular lines is 90 degrees, we can use the concept of alternate angles and the fact that the sum of angles in a straight line is 180 degrees.
1. Let's assume that line L is perpendicular to line M.
2. We can draw a transversal line that intersects both L and M.
3. When a transversal intersects two lines, it creates a pair of alternate angles.
4. Since L and M are perpendicular, the alternate angles created by the transversal will be congruent (equal in measure).
5. Let's label the alternate angles as angle 1 and angle 2.
6. Now, let's consider the straight line formed by line L, the transversal, and line M.
7. The sum of angles in a straight line is 180 degrees.
8. Therefore, angle 1 + angle 2 = 180 degrees.
9. Since angle 1 and angle 2 are congruent, we can rewrite the equation as 2 * angle 1 = 180 degrees.
10. Solving for angle 1, we get angle 1 = 90 degrees.
11. Hence, the measure of the angle between the perpendicular lines L and M is 90 degrees.
Conclusion:
The measure of the angle between two lines perpendicular to each other is always 90 degrees. Therefore, the correct answer is option D) 90.
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