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In this image, two lines, \( m \) and \( n \), are crossed by a transversal, forming two pairs of angles. We are given one of the angles as \( 103^\circ \), and we need to find the value of the angle \( x^\circ \), which is adjacent to this angle.

These angles are formed by the intersection of two lines, and the angle relationships can be identified as supplementary angles. This is because:

- The angle \( 103^\circ \) and \( x^\circ \) are on the same straight line, making them **linear pairs**, meaning they are **supplementary** (their sum is \( 180^\circ \)).

Thus, we can solve for \( x \) using the equation:
\[
103^\circ + x^\circ = 180^\circ
\]

\[
x^\circ = 180^\circ - 103^\circ
\]

Now, let's calculate the value of \( x \).The value of \( x \) is \( 77^\circ \).

Would you like further explanation or details on the concepts? Here are five related questions to explore:

1. What are vertical angles, and how are they used in geometry?
2. Can supplementary angles exist without forming a straight line?
3. How can you identify corresponding angles in a diagram with parallel lines?
4. What is the difference between complementary and supplementary angles?
5. In what scenarios would angles formed by a transversal be congruent?

**Tip:** When dealing with intersecting lines, always check for angle pairs such as vertical, supplementary, or corresponding angles to simplify your solution.

In the image, two lines, m and n, are crossed by a transversal. One of the angles is 103°, and we need to find the adjacent angle x°.

Learn how to solve a geometry problem involving supplementary angles. Two intersecting lines form a linear pair, and one angle is given as 103°. Calculate the adjacent angle x°. This solution involves the supplementary angles theorem, perfect for students in Grades 6-8.

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