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7
v) Sum of angles 5 and 6 is equal to ...
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Answer:
The adjoining star contains a regular pentagon.
So, sum of interior angles =(5−2)×180
o
=540
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In regular polygon, each angle is of same measure
∴ Each interior angle measures 108
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It's supplementary angle measures 180
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−108
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=72
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Now the triangles formed by the star are isosceles, so the othere angle at the base measures 72
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∴ measure of an angle at the vertex will be 180
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−72
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−72
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=36
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∴ Each angle at the vertices of star has a measure of 36
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.
Thus, the sum of all the angle at five vertices of the star =5×36
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=180
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Hence, the answer is 180
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.
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