Question

In the diagram below, P is circumscribed about quadrilateral ABCD.

Find the value of x. Show your work.

Answer 1

So: A + C = 180°
X + 20° + 110° = 180°
Then:
X = 50°

Answer 2

The value of x is 80° .

Explanation:

As shown in the diagram.

The quadrilateral is inscribed in a circle.

Now using the property

Opposite angles in any quadrilateral inscribed in a circle are supplements of each other. (Their measures add up to 180 degrees.)

Thus

∠A + ∠C = 180°

As ∠A = 100° , ∠C = x

Put in the above

100° + x = 180°

x = 180° - 100°

x = 80°