The diagram shows two pairs of parallel lines and transversals, and one of the angles is labeled as $95^\circ$. To find all the angles, we can apply the following geometric principles:

1. Parallel lines and transversals: When a transversal crosses parallel lines, it creates corresponding angles, alternate interior angles, and consecutive interior angles. These angles will have specific relationships, such as being equal or supplementary (sum up to $180^\circ$).

2. Vertical angles: When two lines intersect, the angles opposite each other (vertical angles) are always equal.

Let’s identify the parallel lines and transversals first:

• $MI \parallel XP$ (horizontal lines).
• $KR \parallel YS$ (another set of horizontal lines).
• $IX$ and $RP$ are transversals.

Step-by-step solution:

• Angle $\angle MIA = 95^\circ$ is given.
• Since $MI \parallel XP$ and $IX$ is a transversal, the corresponding angle $\angle XCA$ must also be $95^\circ$ (corresponding angles are equal).
• Similarly, $\angle ARC = 95^\circ$ because alternate interior angles are equal when a transversal crosses parallel lines.
• The angle on the opposite side of $\angle MIA$, $\angle AIB$, is a vertical angle, so $\angle AIB = 95^\circ$.
• The sum of angles on a straight line is $180^\circ$. Therefore, $\angle MAC = 180^\circ - 95^\circ = 85^\circ$.
• By the same logic, $\angle CBD = 85^\circ$ (alternate interior angles with $MAC$).

Thus, we have found the sizes of all the key angles in the diagram:

• $\angle MIA = 95^\circ$
• $\angle XCA = 95^\circ$
• $\angle AIB = 95^\circ$
• $\angle MAC = 85^\circ$
• $\angle ARC = 95^\circ$
• $\angle CBD = 85^\circ$

Would you like a more detailed explanation or any further breakdown of these calculations?

Here are 5 related questions to deepen your understanding:

1. What are the properties of corresponding angles when a transversal crosses parallel lines?
2. How do alternate interior angles help determine unknown angles?
3. What is the relationship between vertical angles?
4. Can you identify supplementary angles in this diagram?
5. How do you verify if two lines are parallel based on angle measurements?

Tip: Always look for parallel lines and transversals in geometric figures. This can help you identify equal or supplementary angles easily.