Question

find the value of a.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $b$ and the $33^{\circ}$ angle are vertical angles, so $b = 33^{\circ}$.

Step2: Use right - angle property

The right - angle formed by the two perpendicular lines is $90^{\circ}$. We know that $a + b=90^{\circ}$.

Step3: Substitute the value of $b$

Since $b = 33^{\circ}$, then $a=90^{\circ}-b$. Substituting $b = 33^{\circ}$ into the equation, we get $a = 90 - 33=57^{\circ}$.

Answer:

$57^{\circ}$