Question

Quadrilateral PQRS is a parallelogram, ∠Q=50°, then what is the measure of ∠S? ​

Answer 1

$\underline{\underline{\textsf{ANSWER :- }}}$

Opposite sides and opposite angles are equal in a parallelogram

More To Know!

✵ Area of parallelogram = Base × Height

✵ Perimeter of parallelogram = 2(a + b)

$\textsc{Properties of Parallelogram}$

❍ Opposite sides are equal.

❍ Opposite angles are equal.

❍ Diagonals bisect each other.

❍ A diagonal of a parallelogram divides it into two triangles of equal area.

✒ Base = Any side of a parallelogram is called its base.

✒ Altitude = The length of the line segment which is perpendicular to the base from the opposite side is called the altitude or height of the parallelogram corresponding to the given base.

$\boxed{\textbf{PROVING OPPOSITE SIDES OF A PARRALELOGRAM ARE EQUAL}}$

Given : Parallelogram PQRS

To prove : ∠P = ∠R and ∠Q = ∠S

Proof :

In parallelogram PQRS ,

Consider,

PS || QR and PQ is transversal

∠P + ∠Q = 180° [Co - int. Angles]⇾(i)

Now, consider AB || DC and BC transversal

∠Q+ ∠R = 180° [Co - int. Angles]⇾ (ii)

From (i) and (ii) we get ;

∠P + ∠Q = ∠Q+ ∠R

∠P= ∠R

∠Q= ∠S

Hence, it is proved.

From the above proof ,

we can come to the conclusion that $\angle S=\angle Q=50^{\circ }$ as the opposite sides of a parallelogram are equal

$\angle S=\angle Q=50^{\circ }$