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m∠LQP=77°
. Find m∠PQR
.



A. 42
B. 70
C. not enough information
D. 38.5

To find the measure of \(\angle PQR\), we can use the fact that the angles on a straight line sum up to 180 degrees. 

Given:
\[ \angle LQP = 77^\circ \]
\[ \angle RQP = 35^\circ \]

We need to find \(\angle PQR\).

Since \(\angle LQP + \angle PQR + \angle RQP = 180^\circ\) (angles on a straight line), we can set up the equation:
\[ 77^\circ + \angle PQR + 35^\circ = 180^\circ \]

Solving for \(\angle PQR\):
\[ 112^\circ + \angle PQR = 180^\circ \]
\[ \angle PQR = 180^\circ - 112^\circ \]
\[ \angle PQR = 68^\circ \]

Therefore, the measure of \(\angle PQR\) is 68 degrees.

The correct answer is not listed among the given choices, so it seems there may be an error in the problem setup or the choices provided.

Would you like further details or have any questions about this solution?

Here are some questions you can ask:
1. Can you explain how to solve for angles on a straight line in more detail?
2. How do we determine the relationships between angles in a geometry problem?
3. What are some common angle relationships used in geometry?
4. Can you provide another example of finding an unknown angle using given angle measures?
5. How do we handle cases where the provided choices don't match our solution?

**Tip:** When dealing with angles on a straight line, always remember that their sum is 180 degrees. This is a key concept in solving many angle-related problems in geometry.

Learn how to find angle PQR when angle LQP is given as 77 degrees and angle RQP is 35 degrees. Understand the concept of angles on a straight line summing to 180 degrees and apply it to solve for angle PQR. Suitable for students in Grades 7-9.

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