Advertisements
Advertisements
प्रश्न
In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°.
Find the value of x.
Advertisements
उत्तर
ABCD is a parallelogram.
⇒ Opposite angles of a parallelogram are congruent.
⇒ ∠DAB = ∠BCD and ∠ABC = ∠ADC = 120°
In ABCD,
∠DAB + ∠BCD + ∠ABC + ∠ADC = 360° ....( sum of the measures of angles of a quadrilateral )
⇒ ∠BCD + ∠BCD + 120° + 120° = 360°
⇒ 2∠BCD = 360° - 240°
⇒ 2∠BCD = 120°
⇒ ∠BCD = 60°
PQRS is parallelogram.
⇒ ∠PQR = ∠PSR = 70°
In ΔCMS,
∠CMS + ∠CSM + ∠MCS = 180° ....( angle sum property )
⇒ x + 70° + 60° = 180°
⇒ x = 50°
APPEARS IN
संबंधित प्रश्न
In the following figure, ABCD is a parallelogram. 
Prove that:
(i) AP bisects angle A.
(ii) BP bisects angle B
(iii) ∠DAP + ∠BCP = ∠APB
In the following figures, find the remaining angles of the parallelogram
In the following figures, find the remaining angles of the parallelogram
In the following figures, find the remaining angles of the parallelogram
Find the measures of all the angles of the parallelogram shown in the figure:
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.
PQR is a triangle formed by the adjacent sides PQ and QR and diagonal PR of a parallelogram PQRS. If in ΔPQR, ∠P : ∠Q : ∠R = 3 : 8 : 4, Calculate the measures of all the angles of parallelogram PQRS.
In the given parallelogram YOUR, ∠RUO = 120° and OY is extended to point S such that ∠SRY = 50°. Find ∠YSR.
