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To solve for \(\angle B\), we can use the following reasoning based on the provided triangle:

We have the following information:
- \(\angle A\) is an exterior angle of the triangle, measured as \(143^\circ\).
- \(\angle C = 61^\circ\).

The exterior angle theorem tells us that the exterior angle \(\angle A\) is equal to the sum of the two non-adjacent interior angles of the triangle, which are \(\angle B\) and \(\angle C\).

Thus, we have the equation:
\[
\angle A = \angle B + \angle C
\]
Substitute the given values:
\[
143^\circ = \angle B + 61^\circ
\]

Solve for \(\angle B\):
\[
\angle B = 143^\circ - 61^\circ = 82^\circ
\]

So, \(\angle B = 82^\circ\).

Would you like more details or have any further questions?

Here are 5 related questions:
1. How can the exterior angle theorem be applied to other triangles?
2. What is the sum of all interior angles in any triangle?
3. How can you find an unknown angle in a right triangle using trigonometric functions?
4. What are supplementary and complementary angles, and how are they different?
5. How does the exterior angle theorem relate to polygon angle sums?

**Tip:** In any triangle, the sum of the three interior angles always adds up to \(180^\circ\). This is useful for solving problems where some angles are unknown.

What is the measure of ∠B in the given triangle where ∠A = 143° (exterior angle) and ∠C = 61°?

Learn how to find the measure of ∠B in a triangle where ∠A = 143° (exterior angle) and ∠C = 61°. This problem covers key geometry concepts such as the Exterior Angle Theorem, suitable for students in Grades 6-8.

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