# 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:

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

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