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Geometry - Triangles

Multiple Choice Questions

81.

G is the centroid of the equilateral Δ ABC, if AB = 9 cm, then AG is equal to:

$3 square root of 3 space cm$
3 cm
^{$fraction numerator 3 square root of 3 over denominator 2 end fraction cm$}
6 cm

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82.
In the figure (not drawn to scale) given below, if AD = DC = BC and $angle BCE space equals space 96 degree$ , then $angle BCE space space equals space 96 degree comma$ then $angle DBC$ is

32°

84°

64°

96°

64°

As we know that in triangle rule property, sum of exterior angle is equal to sum of opposite interior angles
$therefore space space angle BCE space equals space angle CAB space plus space angle ABC 96 space equals space straight x space plus space 2 straight x 96 space equals space 3 straight x straight x space equals space 32 degree$
Thus,
$angle DBC space equals space 2 straight x space equals space 2 space straight x space 32 degree space equals space 64 degree$

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83.

In Δ ABC, $angle straight B space equals space 5 angle straight C$ and $angle straight A space equals space 3 angle straight C$ , then the measure of $angle straight C$ is