# Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9.

Determine the size of the angles of the triangle ΔABC.

Result

A =  27.69 °
B =  27.69 °
C =  124.62 °

#### Solution:

$x=\dfrac{ 180 }{ 2+2+9 }=\dfrac{ 180 }{ 13 } \doteq 13.8462 \ ^\circ \ \\ A=2 \cdot \ x=2 \cdot \ 13.8462=\dfrac{ 360 }{ 13 } \doteq 27.6923 \doteq 27.69 ^\circ \doteq 27^\circ 41'32"$
$B=2 \cdot \ x=2 \cdot \ 13.8462=\dfrac{ 360 }{ 13 } \doteq 27.6923 \doteq 27.69 ^\circ \doteq 27^\circ 41'32"$
$C=9 \cdot \ x=9 \cdot \ 13.8462=\dfrac{ 1620 }{ 13 } \doteq 124.6154 \doteq 124.62 ^\circ \doteq 124^\circ 36'55"$

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