Advertisements
Advertisements
प्रश्न
Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
उत्तर
Let ABCD be a quadrilateral,
Where ∠A = ∠C = 75° and ∠B = ∠D = x ...[say]
Then, by the angle sum property of a quadrilateral, we have
∠A + ∠B + ∠C + ∠D = 360°
⇒ 75° + x + 75° + x = 360°
⇒ 2x = 360° – 150°
⇒ 2x = 210°
⇒ x = 105°
Thus, other two angles are 105° each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.
APPEARS IN
संबंधित प्रश्न
Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
Prove that the diagonals of a parallelogram bisect each other.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between b and c
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between c and f
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.
ABCD is a parallelogram. Find the value of x, y and z.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm)
