https://file.aiquickdraw.com/mathbot/file/1729266703178iuqz35vf.jpg

The problem asks to find the measure of \(\angle WXY\).

From the image, we can see that \(\triangle WXY\) is formed by three angles:
- \(\angle W = 61^\circ\)
- \(\angle Y = 62^\circ\)
- \(\angle X\) is the one we need to find.

We know that the sum of the angles in any triangle is always \(180^\circ\). So, we can set up the equation:

\[
\angle W + \angle Y + \angle X = 180^\circ
\]

Substitute the known values:

\[
61^\circ + 62^\circ + \angle X = 180^\circ
\]

Simplify:

\[
123^\circ + \angle X = 180^\circ
\]

Solve for \(\angle X\):

\[
\angle X = 180^\circ - 123^\circ = 57^\circ
\]

Thus, the measure of \(\angle WXY\) is \(\boxed{57^\circ}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we prove that the sum of interior angles in a triangle is always \(180^\circ\)?
2. How can we calculate an unknown angle if two angles of a triangle are known?
3. What is the significance of exterior angles in a triangle?
4. How would this process change for non-triangular polygons (e.g., quadrilaterals)?
5. How does the triangle inequality theorem relate to angles in triangles?

**Tip**: When solving for an unknown angle in a triangle, always remember that the sum of the angles in any triangle equals \(180^\circ\).

Find the measure of angle WXY in the triangle with angles W = 61°, Y = 62°, and X as the unknown.

Learn how to find the missing angle in a triangle using the angle sum theorem. In this problem, angles W = 61° and Y = 62° are given, and we solve for angle X. Perfect for students in Grades 6-8.

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