Question

Each angle of a square has the measure of ................ degrees.

• A. 60${}^o$
• B. 90${}^o$
• C. 100${}^o$
• D. 360${}^o$

Answer 1

The correct option is B 90${}^o$

$\Rightarrow$ A square is a quadrilateral and we know sum of all four interior angles of a quadrilateral is ${360}^o.$

Let $ABCD$ is a square.

All four sides and four angles of a square are equal.

$\therefore$ $\angle A=\angle B=\angle C=\angle D$ ---- ( 1 )

$\Rightarrow$ $\angle A+\angle B+\angle C+\angle D={360}^o.$

$\Rightarrow$ $\angle A+\angle A+\angle A+\angle A={360}^o$ [ From ( 1 ) ]

$\Rightarrow$ $4\angle A={360}^o$

$\Rightarrow$ $\angle A=\frac{{360}^o}{4}$

$\therefore$ $\angle A={90}^o$

$\Rightarrow$ $\angle A=\angle B=\angle C=\angle D={90}^o$

$\therefore$ Each angle of a square has the measure of ${90}^o.$