Q.If three angles of a quadrilateral are \(\frac{π}{3}\), \(\frac{5π}{6}\), and \(90^\circ\), then write the measure of the fourth angle in both sexagesimal (degree) and circular (radian) units.

\[ \frac{\pi}{3} = \frac{180^\circ}{3} = 60^\circ \quad \text{and} \quad \frac{5\pi}{6} = \frac{5 \times 180^\circ}{6} = 150^\circ \] \[ \therefore \text{Sum of the three angles} = 60^\circ + 150^\circ + 90^\circ = 300^\circ \Rightarrow \text{Fourth angle} = 360^\circ - 300^\circ = 60^\circ \] \[ 60^\circ = 60 \times \frac{\pi}{180} = \frac{\pi}{3} \text{ radians} \] Therefore, the measure of the fourth angle is 60° in sexagesimal (degree) form and \(\frac{\pi}{3}\) radians in circular form.
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