Advertisements
Advertisements
Question
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
Advertisements
Solution
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
RELATED QUESTIONS
Find x in the following figure:
PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
In the given figure, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT = 152°, find x, y and z.
In the given figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD = 146°, find ∠AOB.
The figure formed by joining the mid-points of the adjacent sides of a square is a
The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ∠ABD = 50°, then ∠DPC =
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
If three angles of a quadrilateral are each equal to 75°, the fourth angle is ______.
Sum of all the angles of a quadrilateral is 180°.
