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Geometry - Lines, Angles and Planes

Multiple Choice Questions

The line segment AB intersects the straight line CD at B; AB will be smallest when $angle ABD$ is

$30 degree$
$60 degree$
$90 degree$
$90 degree$

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2.
An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is

14

16

12

18

Sum of interior and exterior angle = 180°
I + E = 180°
Let the exterior angle be x.
$rightwards double arrow space space 5 straight x space plus space straight x space equals space 180 degree rightwards double arrow space space space space space space 6 straight x space equals space 180 degree rightwards double arrow space space space space space space straight x space space equals space 30 degree$
Number of sides of polygon:
$equals space fraction numerator Sum space of space exterior space angle over denominator Each space exterior space angle end fraction space equals space fraction numerator 360 degree over denominator 30 degree end fraction space equals space 12$