Advertisements
Advertisements
प्रश्न
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
उत्तर
We know that, sum of all angles in a quadrilateral is 360°.
If ABCD is a quadrilateral,
∠A + ∠B + ∠C + ∠D = 360° ...(i)
But it is given all angles are equal.
∠A = ∠B = ∠C = ∠D
From equation ...(i)
∠A + ∠A + ∠A + ∠A = 360°
⇒ 4∠A = 360°
∠A = 90°
So, all angles of a quadrilateral are 90°.
Hence, given quadrilateral is a rectangle.
APPEARS IN
संबंधित प्रश्न
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle
In a quadrilateral ABCD, CO and DO are the bisectors of `∠`C and ∠D respectively. Prove that
`∠`COD = `1/2` (`∠`A+ `∠`B).
PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.
Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?
Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.
The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is ______.
The polygon in which sum of all exterior angles is equal to the sum of interior angles is called ______.
