Question

In a regular polygon if the ratio of inner and outer angle is 3:1 then find the difference between the inner and outer angle in the polygon.

• A. 70${}^{\circ }$
• B. 45${}^{\circ }$
• C. 90${}^{\circ }$
• D. 135${}^{\circ }$

Answer 1

The correct option is C

90${}^{\circ }$

Given that the polygon is regular and the ratio of inner and outer angle = 3:1

In the regular polygon , the inner angle + outer angle = 180°

Let the inner angle = 3$x$ and outer angle = $x$

Hence, 3$x$ + $x$ = 180°

4$x$ = 180°

$x$ = 45°

Hence, the measure of the outer angle = 45°

Measure of the inner angle = 45(3) = 135°

Hence, the difference = 135° - 45° = 90°