Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
ABCD is a parallelogram.
Let ∠CAB = x°
Then, ∠ABC = 5x° and ∠BCA = 3x°
In ΔABC,
∠CAB + ∠ABC + ∠BCA = 180° ...(sum of angles of triangle = 180°)
x° + 5x° + 3x° = 180°
9x° = 180°
x° = 20°
⇒ ∠CAB = x° = 20°
⇒ ∠ABC = 5x° = 5 x 20° = 100°
⇒ ∠ BCA = 3x° = 3 x 20° = 60°
Now,
∠ADC = ∠ABC = 100° ...(opposite angles of a parallelogram are equal)
∠ACD =∠CAB = 20° ...(Alternate angles since BC || AD)
∠ CAD = ∠BCA = 60° ...(Alternate angles since BC || AD)
Therefore,
∠ADC= ∠ABC = 100°, ∠ACD + ∠BCA = 80°, ∠CAD + ∠CAB = 80°.
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 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
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:
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.
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
