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If l is parallel to m and p is parallel to Q find a,b,c,d

Given that \( L \parallel M \) and \( p \parallel q \), we can find the angles \( a \), \( b \), \( c \), and \( d \).

1. Since \( L \parallel M \) and the angle \( 60^\circ \) is given, angle \( a \) will be corresponding to the \( 60^\circ \) angle. Hence, \( a = 60^\circ \).

2. Angle \( b \) and angle \( a \) are alternate interior angles because \( p \parallel q \). Therefore, \( b = 60^\circ \).

3. Angles \( a \) and \( c \) are supplementary because they are on a straight line. Thus,
   \[
   a + c = 180^\circ
   \]
   Since \( a = 60^\circ \),
   \[
   60^\circ + c = 180^\circ \implies c = 120^\circ
   \]

4. Similarly, angles \( b \) and \( d \) are also supplementary. Thus,
   \[
   b + d = 180^\circ
   \]
   Since \( b = 60^\circ \),
   \[
   60^\circ + d = 180^\circ \implies d = 120^\circ
   \]

Therefore, the angles are:
- \( a = 60^\circ \)
- \( b = 60^\circ \)
- \( c = 120^\circ \)
- \( d = 120^\circ \)

Would you like details on any part of the solution or have any other questions?

Here are some related questions to further explore the concepts:
1. What are corresponding angles?
2. How are alternate interior angles identified?
3. What is the sum of angles on a straight line?
4. How do parallel lines affect angle relationships?
5. What are supplementary angles?
6. How can you use the properties of parallel lines to find unknown angles?
7. What are vertical angles and how are they calculated?
8. How would the angles change if the parallel lines were not present?

**Tip:** When dealing with parallel lines, remember that corresponding angles, alternate interior angles, and alternate exterior angles are always equal.

Learn how to find angles a, b, c, d when line l is parallel to line m and line p is parallel to line q. This problem covers key geometry concepts involving parallel lines and angle relationships. Suitable for students in Grades 7-9.

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