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To solve for \( x \) in the triangle, we can use the fact that the sum of the interior angles of any triangle is always \( 180^\circ \).

The three angles in the triangle are:
- \( 45^\circ \)
- \( 101^\circ \)
- \( x^\circ \) (which we need to solve for)

So, we can set up the equation:
\[
45^\circ + 101^\circ + x^\circ = 180^\circ
\]

Simplifying:
\[
146^\circ + x^\circ = 180^\circ
\]

Now, subtract \( 146^\circ \) from both sides to solve for \( x \):
\[
x^\circ = 180^\circ - 146^\circ = 34^\circ
\]

Thus, \( x = 34^\circ \).

Would you like more details, or do you have any questions?

Here are five related questions to deepen your understanding:
1. What is the sum of the exterior angles of any triangle?
2. Can a triangle have more than one obtuse angle? Why or why not?
3. How do we classify a triangle based on its angles?
4. If one angle of a triangle is \(90^\circ\), what type of triangle is it?
5. How do angle sums work in polygons other than triangles?

**Tip:** When solving for unknown angles in triangles, always start by recalling that the sum of the angles in any triangle is \(180^\circ\).

The measures of the angles of a triangle are shown in the figure. Solve for x.

Learn how to solve for the unknown angle in a triangle where two angles are given as 45° and 101°. This problem uses the angle sum property of triangles and is suitable for students in Grades 6-8.

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