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 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 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 the following figures, find the remaining angles of the 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.
Find the measures of all the angles of the parallelogram shown in the figure:
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.
The sum of adjacent angles of a parallelogram is ______.
In the given parallelogram YOUR, ∠RUO = 120° and OY is extended to point S such that ∠SRY = 50°. Find ∠YSR.
