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.

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Asked on April 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-24T17:28:31.208Z

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 CD. • CDA = 36^. a) Find BOA. Step 1: Find CAD. Since AD is a diameter, the angle subtended by the diameter at any point on the circumference is 90^. Therefore, ACD = 90^. In ACD, the sum of angles is $180^\

Accepted Answer · 2026-04-24T17:28:31.208Z

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 CD. • CDA = 36^. a) Find BOA. Step 1: Find CAD. Since AD is a diameter, the angle subtended by the diameter at any point on the circumference is 90^. Therefore, ACD = 90^. In ACD, the sum of angles is $180^\

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.

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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.

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