Question

find the value of a and b.

Explanation:

Step1: Use angle - sum property around a point

The sum of angles around a point is $360^{\circ}$. At point $A$, we know some of the angles and can find the unknowns. Also, vertical - angles are equal.

Step2: Find angle $a$

We know that the angle opposite to the $80^{\circ}$ angle and the $35^{\circ}$ angle and $a$ are part of a straight - line (linear pair). Since the sum of angles in a linear pair is $180^{\circ}$, and the angle opposite to the $80^{\circ}$ angle is also $80^{\circ}$ (vertical angles are equal), we have $a=180^{\circ}-80^{\circ}-35^{\circ}$.
$a = 65^{\circ}$

Step3: Find angle $b$

The angle $b$ and the $35^{\circ}$ angle are vertical angles. Vertical angles are equal. So $b = 35^{\circ}$.

Answer:

$a = 65$
$b = 35$