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The base BC of Triangle ABC is produced both ways and the measure of exterior angles formed are 94 degrees and 126 degrees. Then the measure of angle BAC is.

To find the measure of angle \( \angle BAC \) in the triangle \( \triangle ABC \), we can use the properties of exterior angles.

### Given:
- \( \angle ABC = 126^\circ \)
- \( \angle ACB = 94^\circ \)

### Solution:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. 

Here, \( \angle ABC = 126^\circ \) is an exterior angle, so:
\[
\angle BAC + \angle ACB = 126^\circ
\]
We already know that:
\[
\angle ACB = 94^\circ
\]
So,
\[
\angle BAC + 94^\circ = 126^\circ
\]
Subtracting \( 94^\circ \) from both sides, we get:
\[
\angle BAC = 126^\circ - 94^\circ = 32^\circ
\]

Thus, the measure of \( \angle BAC \) is \( 32^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you verify the sum of angles in any triangle?
2. What is the relationship between exterior and interior angles in a polygon?
3. Can you determine the other angles of the triangle if \( \angle BAC \) is known?
4. What are the possible classifications of \( \triangle ABC \) based on its angles?
5. How would the solution change if the exterior angles were different?

**Tip:** Always remember that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Learn how to calculate the measure of angle BAC in triangle ABC using the properties of exterior angles. Given the exterior angles formed are 94 degrees and 126 degrees, discover the step-by-step solution and understand the relationship between exterior and interior angles in triangles. Suitable for students in Grades 7-9.

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