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To find the measure of \(\angle ONM\) in the given triangle \( \triangle MON \), we can use the following approach:

1. **Identify the triangle type**: The triangle \( \triangle MON \) is isosceles, as indicated by the markings on \( \overline{MN} \) and \( \overline{NO} \), meaning \( \overline{MN} = \overline{NO} \).

2. **Base Angles in an Isosceles Triangle**: In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, \(\angle ONM = \angle MON\).

3. **Sum of Angles in a Triangle**: The sum of the interior angles in any triangle is \(180^\circ\).

4. **Set up the equation**: Let the measure of \(\angle ONM = x\). Since \(\angle ONM = \angle MON\), we have:
   \[
   x + x + 25^\circ = 180^\circ
   \]

5. **Solve for \( x \)**:
   \[
   2x + 25^\circ = 180^\circ
   \]
   \[
   2x = 155^\circ
   \]
   \[
   x = 77.5^\circ
   \]

Therefore, the measure of \(\angle ONM\) is \(77.5^\circ\).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How can we determine the third angle in any triangle if we know two angles?
2. What properties distinguish an isosceles triangle from other types of triangles?
3. How does the Exterior Angle Theorem apply to isosceles triangles?
4. Can the same approach be used if the given angle was outside the triangle?
5. What would be the steps if \( \angle ONM \) and \( \angle MON \) had different measures?

**Tip:** Always double-check your angle calculations in isosceles triangles by ensuring the angle sum equals \(180^\circ\).

Find the measure of \(\angle ONM\) in the given triangle \(\triangle MON\), where \(\angle NMO = \angle NOM\) and \(\angle NOM = 25^\circ\).

Learn how to find the measure of an angle in an isosceles triangle \(\triangle MON\), given that one of its base angles is \(25^\circ\). This problem uses the Isosceles Triangle Theorem and Triangle Angle Sum Theorem, perfect for students in Grades 7-9.

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