Question

The alternate Sides of a pentagon are produced to meet so as to form a star shaped figure shown in the given figure.Show that angle x+angle y+angle z+angle t+angle 4 = 180 degrees

Answer 1

Answer:

Each interior angle of regular pentagon =  

5

(5−2)×180  

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​

=108  

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∴ Ext. ∠BAK=Ext.∠ABK=180  

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−108  

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=72  

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∴ In ΔABK,x=180  

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−(72  

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+72  

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)

=180  

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−144  

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=36  

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Similarly, we can show u=t=y=z=36  

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∴∠x+∠y+∠z+∠t+∠u=36  

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×5=180  

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Step-by-step explanation: