# Find the angle CDB if the inscribed angles ADB and ADC rest on circular arcs

Find the angle CDB if the inscribed angles ADB and ADC rest on circular arcs, the degree values of which are 128 and 48, respectively.

1 case. If points C and B are located on opposite sides of the straight line AD.

The arc AB is equal to 128 °, which means that the central angle AOB is equal to 128 °.

The AC arc is 48 °, so the AOC angle is 28 °. The COB central angle is equal to the sum of these two angles: the COB angle is 128 ° + 48 ° = 176 °.

The inscribed angle is equal to half of the central angle resting on the same arc. This means that the CDB angle is 176 °: 2 = 88 °.

2 case. If points C and B are in the same half-plane relative to the straight line AD.

The center angle of the SOC is equal to the difference between the central angles of AOB and AOC. The COB angle is 128 ° – 48 ° = 80 °.

Therefore, the inscribed angle CDB is 80 °: 2 = 40 °.

Answer: 88 ° or 40 °.

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