Find the sum of the given angles in the figure below?

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Answer 1 · 2017-07-29T15:19:24

$180^@$

enter image source here

Draw a line joining vertex $C$ and vertex $D$ , as shown in the figure.

In $DeltaCDH, anglef+angleg+angleh=180^@$
In $DeltaBEH, angleb+anglee+angleh=180^@$
$=> angleb+anglee=anglef+angleg$

In $DeltaACD, anglea+anglec+angled+anglef+angleg=180^@$
$=> anglea+anglec+angled+angleb+anglee=180^@$

Sol. 2) See Fig 2
enter image source here

In $DeltaACG, angleAGC=180-(anglea+anglec)$
$=> angleFGE=anglea+anglec$

In $DeltaBDF, angleBFD=180-(angleb+angled)$
$=> angleGFE=angleb+angled$

In $DeltaEFG, anglea+angleb+anglec+angled+anglee=180^@$

Hnece, the sum of the five interior angles in a 5-point star
$= anglea+angleb+anglec+angled+anglee=180^@$