Angle DAB is an inscribed angle subtending arc DCB.
Angle DOB is a central angle also subtending arc DCB.
An arc subtended by an inscribed angle has the measure of
twice the measure of the inscribed angle, thus arc DCB has measure
2×67° or 134°.
A central angle has the same measure as the measure of its
subtended arc, thus angle DOB also has measure 134°.
Angle DCB is an inscribed angle subtending major arc DAB.
Since a complete circle is an arc of 360°, the measure of
arc DAB is 360°-134° or 226°.
The measure of an inscribed angle is 1/2 the measure of its
subtended arc, so angle DCB has measure 1/2 × 226° or 113°.
Edwin
