Question

One regular polygon has twice as many sides as another.if the ratio of the interior angle of first to second is 5:4 find the number of sides in each polygon

Answer 1

$n \: sided \: regular \: polygon \\ sum \: of \: the \: internal \: angles = (n - 2) \times 180 \\ measure \: of \: each \: internal \: angle = (n - 2) \times 180 \div 2$

$p1 \div p2 = 5 \div 4 \\ p1 = 5x \\ p2 = 4x \\ s1 = (5x - 2)180 \\ s2 = (4x - 2)180$

$i1 = (5x - 2)180 \div 5x \\ = > 36(5x - 2) \div x \: \\ i2 = (4x - 2)180 \div 4x \\ = > 45(4x - 2) \div x$

$36(5x - 2) \div x - 45(4x - 2) \div x = 9 \\ 9 \div x(4(5x - 2) - 5(4x - 2)) = 9 \\ 20x - 8 - 20x + 10 = x \\ x = 2 \\ no.of \: sides \: in \: p1 \: 5x = 5(2) = > 10 \\ no.of \: sides \: in \: p2 \: 4x = 4(2) = > 8$

Follow me❤️