Answer:
Measure of ZA = [tex]90^{o}[/tex]
Step-by-step explanation:
Given: A circle O with AB as diameter. Angle C is inscribed in the circle.
To Find: Measure of ZA.
Solution: AB is a diameter.
∴ Measure of AB = [tex]180^{o}[/tex]
∴ ∠C = [tex]90^{o}[/tex] (Inscribed Angle Theorem)
Measure of ZA = [tex]90^{o}[/tex] (Inscribed angle as well as angle in the same segment of the circle.
Inscribed Angle Theorem: Angle subtended by an arc at the center is double the angle subtended by it at any point on the circumference.
Angle in the Same Segment: Angles in the same segment of the circle are equal.
Angle in a Semi-Circle: An angle in a semi-circle is a right angle.
