Advertisements
Advertisements
प्रश्न
In the following figures, find the remaining angles of the parallelogram
Advertisements
उत्तर
PQRS is a parallelogram with all sides equal and opposite sides parallel.
Hence, PQRS is a Rhombus.
Diagonals of a Rhombus bisect each other.
In ΔPOS,
∠OSP + ∠SPO + ∠POS = 180°
⇒ x + 70° + 90° = 180°
⇒ x = 20°
In ΔQSP,
PS = PQ
⇒ ∠QSP = ∠PQS = x = 20°
And,
∠QSP + ∠PQS + ∠SPQ = 180°
⇒ 20° + 20° + ∠SPQ = 180°
⇒ ∠SPQ = 140°
⇒ ∠SPQ = 140° ....(Opposite angles are equal)
Now,
∠SPQ + ∠SR = 180°
⇒ 140° + PSR = 180°
⇒ ∠PSR = 40°
⇒ ∠PQR = 40° ....(Opposite angles are equal)
Hence,
∠P =∠R = 140° and ∠S = ∠Q = 40°.
APPEARS IN
संबंधित प्रश्न
In a parallelogram `square`ABCD, If ∠A = (3x + 12)°, ∠B = (2x - 32)° then find the value of x and then find the measures of ∠C and ∠D.
In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°.
Find the value of x.
In the given figure, AP is the bisector of ∠A and CQ is the bisector of ∠C of parallelogram ABCD. 
Prove that APCQ is a parallelogram.
In the following figures, find the remaining angles of the parallelogram
In a parallelogram ABCD ∠C = 98°. Find ∠A and ∠B.
The consecutive angles of a parallelogram are in the ratio 3:6. Calculate the measures of all the angles of the parallelogram.
In the given figure, ABCD is a parallelogram, find the values of x and y.
The angles of a triangle formed by 2 adjacent sides and a diagonal of a parallelogram are in the ratio 1 : 5 : 3. Calculate the measures of all the angles of the parallelogram.
If PQRS is a parallelogram, then ∠P – ∠R is equal to ______.
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
