Question

In a regular pentagon $ABCDE$, draw a diagonal $BE$ and then find the measure of $\angle BAE$.
$
  A{.88^0} \\
  B{.108^0} \\
  C{.98^0} \\
  D{.100^0} \\
$

Answer 1

Hint: In the given question, we have to find out the $\angle BAE$, Given figure is a regular pentagon. We know a regular pentagon has five sides & five equal angles. Join, $BE$ and work out the total angles, by using total angles made by a quadrilateral & triangle. Then divide the total angles by its sides. We can find out the value of $\angle BAE$

Complete step-by-step answer:
$ABCDE$ is a regular pentagon, with $BE$ diagonal
     

Since, we know regular pentagon as $5$ equal sides. If $BE$ are joined, we will get a quadrilateral. $BEDC$ & a triangle $BEA$. Quadrilateral makes ${360^0}$& triangle ${180^0}$. A pentagon has ${(360 + 180)^0} = {540^0}$.
A regular pentagon has $5$ equal angles, So each angle of a regular pentagon $ = \dfrac{{540}}{5} = {108^0}$.
Therefore, $\angle BAE$ is an angle of regular hexagon, So its value ${108^0}$

So, the correct answer is “Option B”.

Note: In lower classes, we have learnt about many geometric figures, Polygons are the closed figures with three or more than three sides. Polygons having three sides are TRIANGLE. Polygons having four sides are Quadrilateral, Polygons having five sides are Pentagon and many more. In this question we have to deal with a pentagon whose all sides are equal. For this type of question, one should know the properties of all said figures.