Question

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Answer 1

Given :  A star Shape having 5 vertex angles

To find : Show sum of vertex angle = 2 Right angle

Solution:

there is an integral Pentagon  formed

Sum of angle of pentagon = 540°

using exterior angle of triangle  = Sum of opposite two internal angles

Each Pentagon angle  = one base angle of  triangle + one vertex angle of triangle

Each pentagon angle is exterior angle for two triangles formed with vertex

Hence adding all these pentagon angle twice we get

2 ( 540 )  =   5(180 )  + a + b + c + d + e

=> 1080 = 900 + a + b + c + d + e

=> a + b + c + d + e = 180°

=>  a + b + c + d + e = 2 * 90°

= 2 right angle

QED

Hence proved

Learn more:

In the diagram, SHAPE is a regular pentagon. The sides SHand PA ...

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