https://file.aiquickdraw.com/mathbot/file/1725469585278zp2ir0mr.jpg

The image shows a geometric diagram with angles and sides labeled. The problem is asking for the measure of angle \( \angle BAC \) based on the given information.

Here’s what I see in the image:
- The triangle \( \triangle ABC \) is formed by points \( A \), \( B \), and \( C \).
- \( \angle BAC \) is the angle we need to find.
- The given angles are \( \angle ABC = 52^\circ \) and \( \angle ACB = 79^\circ \).
  
Since the sum of angles in a triangle is always \( 180^\circ \), we can calculate \( \angle BAC \) as follows:

\[
\angle BAC = 180^\circ - \angle ABC - \angle ACB
\]
\[
\angle BAC = 180^\circ - 52^\circ - 79^\circ = 49^\circ
\]

So, the measure of \( \angle BAC \) is \( 49^\circ \).

Would you like more details on the solution, or do you have any other questions?

### Follow-up Questions:
1. What are the properties of the angles in a triangle?
2. How can you check if your answer to an angle problem is correct?
3. What happens if two angles in a triangle are equal?
4. Can the angles of a triangle be more than \( 180^\circ \)?
5. How can trigonometric identities be used to solve for angles in a triangle?

### Tip:
When solving problems involving the sum of angles in a triangle, always remember that the total must be \( 180^\circ \). This is a fundamental property that can be used to solve for unknown angles.

What is the measure of \( \angle BAC \) in the triangle, given \( \angle ABC = 52^\circ \) and \( \angle ACB = 79^\circ \)?

Learn how to calculate the measure of \( \angle BAC \) in a triangle when given \( \angle ABC = 52^\circ \) and \( \angle ACB = 79^\circ \). This problem demonstrates the use of the Triangle Angle Sum Theorem, suitable for students in Grades 6-8.

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