Progression...

Number Theory Level pending

In the given figure, measures of $\angle AOB, \angle BOC$ and $\angle COD$ form an Arithmetic progression . If the smallest angle, $\angle AOB = 20^ \circ$ , find $\angle BOC$ and $\angle COD$ .

65^ \circ

and

95^ \circ

70^ \circ

and

120^ \circ

50^ \circ

and

80^ \circ

60^ \circ

and

100^ \circ

1 solution

Rick B
Sep 3, 2014

$\angle AOB + \angle BOC + \angle COD = 180^\circ$ and, since it's an AP, $\angle BOC = 20^\circ + x$ and $\angle COD = 20^\circ + 2x$

So we have $20^\circ + 20^\circ + x + 20^\circ + 2x = 60^\circ + 3x = 180^\circ \implies 3x = 120^\circ \implies x = 40^\circ$

So $\angle BOC = 20^\circ + 40^\circ = \boxed{60^\circ}$ and $\angle COD = 20^\circ + 80^\circ = \boxed{100^\circ}$

Progression...

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