In this diagram, you are tasked with finding the values of angles $a$ and $b$. The diagram shows several lines intersecting at point $A$, creating different angles. Here's how we can approach the problem:

Step 1: Identify known angles and relationships

• The angle labeled $25^\circ$ is provided between lines $E$ and $F$.
• It is clear from the figure that lines $F$ and $D$, $E$ and $B$, as well as other pairs, are forming vertically opposite angles or linear pairs.

Step 2: Use the linear pair rule

A linear pair of angles on a straight line always sums to $180^\circ$. Let's apply this concept:

• Angle $a$ and $25^\circ$ form a linear pair since they lie on the same straight line. Therefore: $a + 25^\circ = 180^\circ$ Solving for $a$: $a = 180^\circ - 25^\circ = 155^\circ$

Step 3: Use the vertical angles rule

• Angle $b$ is vertically opposite to the angle adjacent to $a$, meaning: $b = 90^\circ$ This is because line $BC$ is perpendicular to line $EF$, creating a right angle ($90^\circ$).

Final Values:

• $a = 155^\circ$
• $b = 90^\circ$

Would you like further explanation on the reasoning behind vertical angles or linear pairs?

Related questions:

1. What is the sum of all angles around point $A$?
2. How do we know that $BC$ is perpendicular to $EF$?
3. Can angles $a$ and $b$ ever change without modifying the lines?
4. What would the relationship between $a$ and $b$ be if they were on the same side of a straight line?
5. Can you calculate the value of any other angles in the diagram using these methods?

Tip:

Always look for linear pairs and vertical angles when dealing with intersecting lines—they simplify many angle calculations.