Question

One angle of a square measure 90 degree . Find the measurements of the other three angles and explain your answer.

Answer 1

$\star \textbf{QUESTION}\star$

One angle of a square measure 90 degree . Find the measurements of the other three angles and explain your answer.

$\star\bf{SOLUTION}\star$

⇒  A square is a quadrilateral and we know sum of all four interior angles of a quadrilateral is 360 °

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

∴ ∠A = ∠B = ∠C = ∠D = 360°  ... (1)

Let ABCD is a square.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°           [ From ( 1 ) ]

⇒ 4∠A = 360°

⇒ ∠A = ${\frac{360}{4} }$

∴   ∠A = 90°

⇒ ∠A = ∠B = ∠C = ∠D = 90°

∴  Each angle of a square has the measure of 90°

so....according to this the angle of the three other sides measures 90° each.

Answer 2

Answer:

\star \textbf{QUESTION}\star⋆QUESTION⋆

One angle of a square measure 90 degree . Find the measurements of the other three angles and explain your answer.

\star\bf{SOLUTION}\star⋆SOLUTION⋆

⇒  A square is a quadrilateral and we know sum of all four interior angles of a quadrilateral is 360 °

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

∴ ∠A = ∠B = ∠C = ∠D = 360°  ... (1)

Let ABCD is a square.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°           [ From ( 1 ) ]

⇒ 4∠A = 360°

⇒ ∠A = {\frac{360}{4} }4360

∴   ∠A = 90°

⇒ ∠A = ∠B = ∠C = ∠D = 90°

∴  Each angle of a square has the measure of 90°

so....according to this the angle of the three other sides measures 90° each.