If the ratio of the angles of a quadrilateral is 2 : 7 : 2 : 7, then it is a:
parallelogram
The angles add up to 360°, and 2 + 7 + 2 + 7 = 18 parts, so one part = 20°.
The angles, taken in order, are 40°, 140°, 40° and 140°.
Opposite angles are equal and adjacent angles add up to 180°, so the quadrilateral is a parallelogram; it is not a rectangle or square, whose angles are all 90°.
Hence, the answer is parallelogram.
Similar Questions
In a cyclic quadrilateral ABCD, the sides are AB = 10 cm, BC = 14 cm, CD = 8 cm, and DA = 12 cm. Find the area of the quadrilateral.
In a quadrilateral ABCD, \(\angle A = 32^\circ\) and \(\angle B = 58^\circ\). The bisectors of \(\angle C\) and \(\angle D\) meet at O. What is the measure of \(\angle DOC\)?
In a trapezium ABCD, AB∥CD and AB = 16 cm, CD = 8 cm. What is the ratio of the areas of ΔABC and ΔACD?
In a parallelogram ABCD, the diagonals intersect at O. ∠BCA = 38° and ∠CAB = 27°. Find ∠AOD if ∠ADO : ∠CDO = 2 : 3.
Consider an equilateral quadrilateral whose angle bisectors intersect at right angles. One side of the quadrilateral measures 10 cm, and one of its perpendicular diagonals is 12 cm. Find half of the area of the quadrilateral.
In quadrilateral PQRS, ∠P = 105°, ∠Q = 65° and ∠R = ∠S. Find the measure of 2∠P + ∠S − ∠Q.
Important Questions from Quadrilaterals
The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be
The side of a rhombus is 26 cm. The length of one of its diagonals is 20 cm. The sum of the lengths of the diagonals of this rhombus is equal to the perimeter of a rectangle. If the difference between the length and breadth of the rectangle is 6 cm, then what is the area of the rectangle?
PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
ABCD is a trapezium in which AB || DC and DC is perpendicular to BC. If ∠DAB = 110°, then ∠ABC - ∠ADC =_____.
The adjacent angles of a rhombus are in the ratio of 3 : 6. The smallest angle of the rhombus is:
