Answer:
See explanation
Step-by-step explanation:
The given circle has center O.
A, B,C, and D are points on the circumference of the circle.
We want to prove that: [tex]\angle A\cong \angle D[/tex]
We need to join to B and C as shown in the attachment.
Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.
This implies that:
[tex] \angle O=2\angle A...(1)[/tex]
[tex]\angle O=2\angle D...(2)[/tex]
The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.
This implies that:
[tex]2\angle A=2\angle D[/tex]
[tex]\therefore \angle A\cong \angle D[/tex]
