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Geometry - Lines, Angles and Planes

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Question
SSCCGLENQA12042640
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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

Solution

C.

12

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

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Question
SSCCGLENQA12042703
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In a triangle ABC,
angle straight A space plus space 1 half angle straight B space plus space angle straight C space equals space 140 degree, then angle straight B is

  • 50°

  • 80°

  • 40°

  • 60°

Solution

B.

80°

angle straight A space plus space angle straight B space plus space angle straight C space equals space 180 degree space space space space space space space space... left parenthesis straight i right parenthesis angle straight A space plus space fraction numerator angle straight B over denominator 2 end fraction space plus space angle straight C space equals space 140 degree space space space space space space... left parenthesis ii right parenthesis
By equations (i) - (ii),
fraction numerator angle straight B over denominator 2 end fraction space equals space 180 degree space minus space 140 degree
rightwards double arrow space space fraction numerator angle straight B over denominator 2 end fraction space equals space 40 degree rightwards double arrow space space angle straight B space equals space 80 degree

Question
SSCCGLENQA12042358
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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
  • 45 degree

Solution

C.

90 degree

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