In a circle with center O and points A, B, C, D on the circumference, AD is a diameter and BO is parallel to CD. If angle CDA is 36 degrees, find angle BOA.

Here's a step-by-step solution for each part of Example 25:

Given information:

• Circle with center $O$.
• $A, B, C, D$ are points on the circle.
• $AOD$ is a straight line, which means $AD$ is a diameter.
• $BO \parallel CD$.
• $\angle CDA = 36^\circ$.

a) Find $\angle BOA$.

Step 1: Find $\angle CAD$.
Since $AD$ is a diameter, the angle subtended by the diameter at any point on the circumference is $90^\circ$. Therefore, $\angle ACD = 90^\circ$.
In $\triangle ACD$, the sum of angles is $180^\