Inscribed Quadrilateral

Inscribed Quadrilateral

How to solve inscribed quadrilateral problems: formula, example, and its solution.

Formula

For an inscribed quadrilateral, the opposite angles are supplementary.

In an inscribed quadrilateral,
there are two pairs of opposite angles.
(left figure, right figure)

For each pair,
the opposite angles are supplementary.

So m∠[blue] + m∠[green] = 180.

Supplementary angles

Example

Find the value of x. The measures of the interior angles of an inscribed quadrilateral: x, y, 100, 70.

The given angles are the interior angles
of an inscribed quadrilateral.

These two angles are the opposite angles.

So x + 100 = 180

Move +100 to the right side.

Then x = 80.

These two angles are also the opposite angles.

So 70 + y = 180.

Move 70 to the right side.

Then y = 110.