The quadrilateral ABCD is inscribed in a circle with the AC diameter. Find the angles

| March 8, 2021 | education

The quadrilateral ABCD is inscribed in a circle with the AC diameter. Find the angles of this quadrilateral if BC = 100 degrees; CD = 60 degrees.

The inscribed angle BAC rests on the arc BC, the degree measure of which is 100, then the angle BAC is equal to half the degree measure of this arc, the angle BAC = 100/2 = 50.

Similarly, the angle DAC is equal to half of the degree measure of the arc CD. Angle DАС = 60/2 = 30.

Then the angle BAD = BAC + DAC = 50 + 30 = 80.

The sum of the opposite angles of a quadrilateral inscribed in a circle is 180, then the angle ВСD = (180 – BAD) = (180 – 80) = 100.

The inscribed angles ABC and ADC are based on the diameter of the AC circle, then their degree measure is 90.

Answer: The angles of the quadrilateral are 80, 90, 100, 90.



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