Given:
In the circle, and
.
To find:
The following measures:
(a)
(b)
Solution:
According to the central angle theorem, the central angle is always twice of the subtended angle intercepted on the same same arc.
In a cyclic quadrilateral, the opposite angles are supplementary angles.
UVWX is a cyclic quadrilateral. So,
[Opposite angles of a cyclic quadrilateral]
Now,
[Opposite angles of a cyclic quadrilateral]
Therefore, and
.