Math Problem Statement

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

Solution

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

Here’s what I see in the image:

  • The triangle ABC\triangle ABC is formed by points AA, BB, and CC.
  • BAC\angle BAC is the angle we need to find.
  • The given angles are ABC=52\angle ABC = 52^\circ and ACB=79\angle ACB = 79^\circ.

Since the sum of angles in a triangle is always 180180^\circ, we can calculate BAC\angle BAC as follows:

BAC=180ABCACB\angle BAC = 180^\circ - \angle ABC - \angle ACB BAC=1805279=49\angle BAC = 180^\circ - 52^\circ - 79^\circ = 49^\circ

So, the measure of BAC\angle BAC is 4949^\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 180180^\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 180180^\circ. This is a fundamental property that can be used to solve for unknown angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angles

Formulas

Sum of angles in a triangle: \( \angle BAC = 180^\circ - \angle ABC - \angle ACB \)

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8