https://file.aiquickdraw.com/mathbot/file/1726388665558i4c4whm6.jpg

Let's analyze each part of the image to find the value of \( x \) in each diagram.

### Diagram a:
- The two lines are parallel, and we have a transversal intersecting them.
- The angle \( x^\circ \) and the 110° angle are alternate interior angles.
- By the alternate interior angle theorem, alternate interior angles are equal when two lines are parallel.
  
Thus, 
\[
x^\circ = 110^\circ.
\]

### Diagram b:
- The sum of the angles on a straight line is 180°. The given angles form a full circle around a point, so the sum of all the angles must be 360°.
- The given angles are 130°, \( x^\circ \), and 280°.
  
So, the equation is:
\[
130^\circ + x^\circ + 280^\circ = 360^\circ.
\]
Simplifying this:
\[
x^\circ + 410^\circ = 360^\circ,
\]
\[
x^\circ = 360^\circ - 410^\circ,
\]
\[
x^\circ = -50^\circ.
\]
Since this angle would actually be the reflex angle (the external angle), we convert it to positive:
\[
x = 50^\circ.
\]

### Diagram c:
- The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- The exterior angle given is 140°, and the interior angles are 100° and \( x^\circ \).

Using the exterior angle theorem:
\[
140^\circ = 100^\circ + x^\circ,
\]
\[
x^\circ = 140^\circ - 100^\circ,
\]
\[
x

Find the value of x in each of these diagrams.

Learn how to find the value of x in geometric diagrams involving alternate interior angles, sum of angles around a point, and exterior angle theorem. This problem is suitable for students in Grades 7-9 and covers key geometric concepts.

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