Advertisements
Advertisements
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.
Advertisements
उत्तर
Given: ∠A = (3x + 12)˚ and ∠B = (2x - 32)˚
Opposite angles of a parallelogram are equal.
∴ ∠C = ∠A ...(i)
⇒ ∠C = (3x + 12)˚
∠D = ∠B …(ii)
∠D = (2x - 32)˚
In a quadrilateral, the sum of all the angles is equal to 360˚.
∴ In `square`ABCD,
∠A + ∠B + ∠C + ∠D = 360˚
∴ 3x + 12 + 2x - 32 + 3x + 12 + 2x - 32 = 360
∴ 10x - 40 = 360
∴ 10x = 360 + 40
∴ 10x = 400
∴ x = `400/10`
∴ x = 40
∴ ∠A = (3x + 12)˚
⇒ ∠A = 3 × 40 +12
⇒ ∠A = 120 + 12
⇒ ∠A = 132˚
∴ ∠C = 132˚ ...[From (i)]
∴ ∠B = (2x - 32)˚
⇒ ∠B = 2 × 40 - 32
⇒ ∠B = 80 - 32
⇒ ∠B = 48˚
∴ ∠D = 48˚ ...[From (ii)]
Hence, the measure of x is 40.
Also, measures of ∠C and ∠D are 132˚ and 48˚ respectively.
APPEARS IN
संबंधित प्रश्न
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 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 a parallelogram ABCD ∠C = 98°. Find ∠A and ∠B.
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.
Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, determine CD.
If PQRS is a parallelogram, then ∠P – ∠R is equal to ______.
The sum of adjacent angles of a parallelogram is ______.
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
In the given parallelogram YOUR, ∠RUO = 120° and OY is extended to point S such that ∠SRY = 50°. Find ∠YSR.
