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

In this triangle, we are given two of the angles: \( 45^\circ \) and \( 101^\circ \). The third angle is \( x^\circ \).

We can use the following equation:

\[
45^\circ + 101^\circ + x^\circ = 180^\circ
\]

Simplifying:

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

Subtract \( 146^\circ \) from both sides:

\[
x^\circ = 180^\circ - 146^\circ
\]

\[
x^\circ = 34^\circ
\]

Thus, the value of \( x \) is \( 34^\circ \).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand on this:

1. What is the sum of interior angles in any polygon with \( n \) sides?
2. How can you find an unknown angle if you know two angles in a right triangle?
3. Can triangles have angles greater than \( 180^\circ \) in total?
4. What is the difference between acute, obtuse, and right angles in triangles?
5. How can exterior angles of a triangle be used to find the interior ones?

**Tip:** In any triangle, the sum of the three interior angles will always be \( 180^\circ \), regardless of the type of triangle.

The measures of the angles of a triangle are shown in the figure below. Solve for x, where one angle is 45° and another angle is 101°.

Learn how to find the unknown angle in a triangle where two angles are given as 45° and 101°. This problem covers geometric concepts, such as the angle sum property, and is suitable for students in Grades 6-8.

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