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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 3
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  • #8
    The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find : (i) measure of each interior angle ; (ii) measure of each exterior angle and (iii) number of sides in the polygon.
    Ans : Let exterior angle = x°
    Interior angle = 5x°
    x + 5x = 180°
    ⇒ 6x = 180°
    ⇒ x = 30°
    Each exterior angle = 30°
    Each interior angle = 5 x 30° = 150°
    Let no. of sides = n
    ∵ each exterior angle = 360˚/n
    30Ëš = 360Ëš/n
    ⇒ n = 360˚/30˚
    ⇒ n = 12
    Hence, (i) 150Ëš (ii) 30Ëš (iii) 12