Advertisements
Advertisements
Question
In the given figure, ABCD is a parallelogram, find the values of x and y.
Advertisements
Solution
ABCD is a parallelogram.
Opposite angles of a parallelogram are equal.
∴ ∠A = ∠C
⇒ 4x + 3y - 6 = 9y + 2
⇒ 4x - 6y = 8
⇒ 2x - 3y = 4 ....(i)
AB || CD and AD is the transversal.
∴ ∠A + ∠D = 180° ....(Co-interior angles are supplementary)
⇒ (4x + 3y - 6) + (6x + 22) = 180°
⇒ 10x + 3y + 16 = 180°
⇒ 10x + 3y = 164 ....(ii)
Adding equations (i) and (ii), we get
12x + = 168
⇒ x = 14
Substituting the value of x in (i), we get
2 x 14 - 3y = 4
⇒ 28 - 3y = 4
⇒ 3y = 24
⇒ y = 8
Hence, x = 14 and y = 8.
APPEARS IN
RELATED QUESTIONS
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 case of a parallelogram
prove that:
(i) The bisectors of any two adjacent angles intersect at 90o.
(ii) The bisectors of the opposite angles are parallel to each other.
In the following figures, find the remaining angles of the parallelogram
In the following figures, find the remaining angles of the parallelogram
The consecutive angles of a parallelogram are in the ratio 3:6. Calculate the measures of all the angles of the parallelogram.
Find the measures of all the angles of the parallelogram shown in the figure:
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.
If PQRS is a parallelogram, then ∠P – ∠R is equal to ______.
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
