Question

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?

x > 38
x < 39
x < 77
x > 103

Answer 1

To find the value of \( x \), which is the measure of the exterior angle \( \angle PNM \), we can use the properties of angles in triangles, specifically the Exterior Angle Theorem.

According to the Exterior Angle Theorem, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. In this case:

\[
x = \angle NPO + \angle PON
\]

From the problem statement:
- \( \angle NPO = 38^\circ \)
- \( \angle PON = 39^\circ \)

Adding these angles together:

\[
x = 38^\circ + 39^\circ = 77^\circ
\]

Now, we will evaluate each of the given statements about \( x \):

1. **x > 38**:
- \( 77 > 38 \) is true.

2. **x < 39**:
- \( 77 < 39 \) is false.

3. **x < 77**:
- \( 77 < 77 \) is false.

4. **x > 103**:
- \( 77 > 103 \) is false.

The only true statement about \( x \) is:

\[
x > 38
\]

Hence, the correct conclusion is that \( x > 38 \).