3 years ago

Quadrilateral ABCD is inscribed in a circle.

1 answer:

6 0

In general, the sum of the measures of the interior angles of a quadrilateral is 360. This is true for every quadrilateral. This does not help here, because there are two angles (angles B and D) we know nothing about. We only know about opposite angles A and C.

In this case, you can use another theorem.
Opposite angles of an inscribed quadrilateral are supplementary.

m<A + m<C = 180

3x + 6 + x + 2 = 180

4x + 8 = 180

4x = 172

x = 43

m<A = 3x + 6 = 3(43) + 6 = 135

Answer: 135 deg

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Quadrilateral ABCD ​ is inscribed in a circle.

Quadrilateral ABCD is inscribed in a circle.