https://file.aiquickdraw.com/mathbot/file/1725626667026brt9cb3x.jpg

The image shows a triangle \( \triangle ABC \) with a line \( BD \) extending from point \( B \). We are given:

- Angle \( \angle BAC = 58^\circ \)
- Angle \( \angle ABC = x \)
- Line \( BD \) is a straight line, forming an exterior angle \( \angle CBD = x \).

Since \( BD \) is a straight line, we know that:

\[
\angle ABC + \angle CBD = 180^\circ
\]

The angle \( \angle ABC \) is an exterior angle to the triangle, so it equals the sum of the two opposite interior angles \( \angle BAC \) and \( \angle ACB \). Hence,

\[
x = \angle BAC + \angle ACB
\]

We know \( \angle BAC = 58^\circ \), and since the sum of all angles in a triangle is \( 180^\circ \), we can find \( \angle ACB \) by subtracting:

\[
\angle ACB = 180^\circ - (58^\circ + \angle ABC)
\]

Let me calculate \( x \) for you.The measure of angle \( \angle ACB \) is \( 122^\circ \).

Since the exterior angle \( \angle ABC = x \) is the sum of the two opposite interior angles, we can now state:

\[
x = 58^\circ + 122^\circ = 180^\circ
\]

Thus, the value of \( x \) is \( 180^\circ \).

Would you like more details or further explanation?

Here are some related questions for you:
1. How is the exterior angle theorem used in different triangle types?
2. What is the sum of the interior angles in a polygon?
3. Can the exterior angle theorem be applied to non-triangular polygons?
4. How do you calculate the interior angles of an isosceles triangle?
5. How would you find \( x \) if one of the other angles was unknown?

**Tip:** Remember that the exterior angle of a triangle is always equal to the sum of the two opposite interior angles.

Find the value of angle x in the given triangle configuration where angle BAC = 58° and BD is a straight line.

Learn how to solve for the exterior angle x in a triangle where angle BAC is 58° using the exterior angle theorem. A step-by-step solution is provided with key concepts about triangle angles and their relationships. Suitable for students in Grades 8-10.

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