Question

Identify the equiangular polygon(s).

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B), (D)

An equiangular polygon is a polygon that has all the interior angles of same measure.

Let's go through each option one by one.

Option (a): It is an equilateral triangle. Hence, all the interior angles are equal in measure i.e. ${60}^o$

Option (b): It is a rectangle. Hence, all the interior angles are ${90}^o.$

Option (c): It is a rhombus. From the figure, it can be seen that adjacent interior angles are unequal.

Option (d): It is a pentagon.

Interior angle $\angle A={180}^o-{72}^o={108}^o$
Similarly, $\angle C={108}^o.$

Also, sum of interior angles $=(n-2)\times {180}^o$
where $n$ is the total number of sides, here it is 5.

$\therefore$ Sum of interior angles $=(5-2)\times {180}^o$
$=3\times {180}^o$
$={540}^o$

$\Rightarrow \angle A+\angle B+\angle C+\angle D+\angle E={540}^o$
$\Rightarrow 4\times {108}^o+\angle E={540}^o$
$\Rightarrow \angle E={540}^o-4\times {108}^o={108}^o$
$\therefore$ All the interior angles are equal.

Only option (c) is wrong.