Parallelogram ABCD is inscribed in a circle. Then, the measure of angle A must be 90?
In a cyclic quadrilateral, opposite pairs of interior angles are always supplementary - that is, they always add to 180°.
Now, what do you know about opposite angles of a parallelogram?
No, the measure of angle A in a parallelogram inscribed in a circle does not necessarily have to be 90 degrees.
To determine whether the measure of angle A in parallelogram ABCD is 90 degrees, we need to consider the properties of parallelograms.
A parallelogram is a quadrilateral where opposite sides are parallel. Inscribe a parallelogram ABCD inside a circle. Since parallel lines do not intersect, the opposite sides of the parallelogram would not intersect inside the circle either.
Now, let's focus on angle A. If angle A is 90 degrees, then side AD will be diametrically opposite to side BC. In this case, if we draw the diameter of the circle that passes through A and C, the diameter will be perpendicular to side BC, and AD will be its chord.
However, it is important to note that a parallelogram inscribed in a circle does not necessarily have a right angle or a vertex on the diameter. This means that angle A in parallelogram ABCD can have any measure, except 90 degrees, given the properties of parallel lines and circles.
Therefore, the measure of angle A in parallelogram ABCD does not have to be 90 degrees.