Question

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

Answer 1

`180^@`

Explanation:

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

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^@`