Advertisements
Advertisements
प्रश्न
The angles A, B, C and D of a trapezium ABCD are in the ratio 3: 4: 5: 6. Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer.
Advertisements
उत्तर
As the trapezium ABCD is a quadrilateral,
∴ Sum of its interior angles = 360°
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ 3x + 4x + 5x + 6x = 360°
⇒ 18x = 360°
⇒ x = `360^circ/18 = 20°`
∴ ∠A = 3x = 3 × 20° = 60°
and ∠B = 4x = 4 × 20° = 80°
and ∠C = 5x = 5 × 20° = 100°
and ∠D = 6x = 6 × 20° = 120°
AB is parallel to DC.
∵ ∠A + ∠D = 180°
∠A and ∠D are co-interior angles whose sum = 180°
APPEARS IN
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of opposite sides are there?
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of opposite angles are there?
Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.
Complete the following statement by means of one of those given in brackets against each:
f consecutive sides of a parallelogram are equal, then it is necessarily a ..................
In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =
In a pentagon ABCDE, AB || ED and ∠B = 140°, ∠C = 2x° and ∠D = 3x°. Find ∠C and ∠D
In quadrilateral HOPE, the pairs of opposite sides are ______.
Using the information given, name the right angles in part of figure:
BA ⊥ BD
Using the information given, name the right angles in part of figure:
AC ⊥ BD
