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In a quadrilateral the angles are in the ratio 3:4:5:6. Then the difference between the greatest and the smallest angle is
Let the angles be
Difference
The angles of a quadrilateral are \(\mathrm{x^o,x10^o,x+30^o}\) and \(\mathrm{2x^o}\). Find the greatest angle.
Greatest angle
A quadrilateral in which both pairs of opposite sides are parallel is a
parallelogram.
ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are joined if \(\angle CAD=50^o\) and \(\angle BDC=45^o\) Find \(\angle BCD\)
(Angles in same
segment)
In the given figure, ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are joined if \(\angle CAD=40^o\) and \(\angle BDC=25^o\). Find \(\angle BCD\)
ABCD is a cyclic quadrilateral so the sum
of opposite angles is
In the given figure, ABCD is a cyclic quadrilateral in which \(\angle BAD=120^o\) find \(\angle BCD\)
In the given figure, PQ is a diameter of a circle with centre O and PQRS is a cyclic quadrilateral. SQ is joined If \(\angle R=138^o\) find \(\angle PQS\).
Angle in a semicircle is
So,
In
Two circles intersect in A and B. Quadrilateral PCBA and ABDE are inscribed in these circles such that PAE and CBD are line segments. If \(\angle P=95^o\) and \(\angle C=40^o\) find the value of Z.
In PABC
In ABDE,
ABCD is a quadrilateral. AB=BC=CD=DA and \(\angle A=\angle B=\angle C=\angle D=90^o\). Then ABCD can be called
ABCD can be rhombus, square or a
parallelogram.
If ABCD is a quadrilateral and E, F, G, H are the midpoints of AB, BC, CD and DA respectively then EFGH is a
Parallelogram
The number of sides of a regular polygon whose each exterior angle has a measure of \(30^o\) is
Let the number of sides be n
RSTU is a parallelogram as shown in the figure below. Then the shown angles x and y are related.
RSU and STU are congruent but x and y are
not corresponding angles.
If a quadrilateral has two adjacent sides equal and the other two sides equal is called
Kite
In the given figure, line RT is drawn parallel to SQ. If \(\angle QPS=100^o,\ \angle PQS=40^o\angle PSR=85^o\) and \(\angle QRS=70^o\) then \(\angle QRT=\)
(corresponding
angles)
Which of the following can never be the measure of exterior angle of a regular polygon?
can never be the measure.
ABCD is a parallelogram. Find the angles x, y, z
Since ABCD is a parallelogram
In
From
In FCD
In parallelogram ABCD
The diameter of circumcircle of a rectangle is 10 cm and breadth of the rectangle is 6 cm. Its length is
In a parallelogram ABCD, If AB = 2X + 5, CD = y+1, AD = y+5, BC = 3x4 then ratio of AB:BC is
AB = CD (opposite sides of a parallelogram
are equal)
and
and
Adding both the equations,
The diagonals of a parallelogram ABCD intersect at O. If \(\angle BOC=90^o\) then \(\angle AOB\) is
If two adjacent angles of a parallelogram are in the ratio 3:2 then the measure of the angles are
Let the angles be 3x and 2x
Rohit has 6 wooden sticks of equal length. He wants to join all of them in such a way that they make a regular polygon. At what internal angle he has to join wooden stick with each other?
Interior angle
n = number of sides of the polygon here, n = 6
DO and CO are the bisectors of \(\angle ADC\) and \(\angle BCD\) respectively. If \(\angle ADC=\angle BCD=60^o\) and \(\angle DAB=100^o\). Find the measure of \(\angle DOC\) and \(\angle ABC\) respectively.
In
In ABCD
Vikasâ€™s garden is in the form of a parallelogram whose one side is 4.8 cm and other side is \(1\dfrac{1}{2}\) times of this side. He wants to fence his garden four times by a wire. Find the length of the wire required.
Length of wire required
perimeter of parallelogram
Which of the following quadrilateral is not a parallelogram?
Kite is not a parallelogram
Find the total area of shaded region
Area
Area of square
ABCD is a rhombus and ALMC is a square, AC=BC. Find âˆ MBC
ABCD is a rhombus.
Also, ALMC is a square
AL = LM = MC = CA
Also AC = BC
is an equilateral triangle.
Now (each angle is a square)
AS, and So,
In
What is the area of trapezoid in square units?
The number of sides of a regular polygon is double that of another and the magnitude of its angle is also double that of the other. Find the number of sides of the polygon.
Let be the first polygon and p2 be the
second polygon.
Let n be the number of side of and 2n be the number of side of
Let Q, be the magnitude of angle of and be the magnitude of angle of
From equation (1)
Which of the following is not true for an exterior angle of a regular polygon with n sides.
Each exterior angle
The angles P, Q, R, S of a quadrilateral are in the ratio 1:3:7:9 Then PQRS is a
Let the angles be
The angles are
As,
So, PQRS
It is a trapezium with PQRS
The sum of angles of a concave quadrilateral is
Sum of angle of a concave quadrilateral is equal to
How many nonoverlapping triangles can we make in a ngon (polygon having n sides) by joining the verticals.
(n2) nonoverlapping triangles can be made.
The interior angle of a regular polygon exceeds the exterior angle by 132Â° . The number of sides in the polygon is
Let the number of sides of polygon = n
Interior angle
Exterior angle
AIQ
For what value of x is the perimeter of shape 186 cm?
Perimeter
How many sides does a regular polygon have, whose interior angle is eight times its exterior angle?
Interior angle Exterior angle
Given,
Any cyclic parallelogram having unequal adjacent sides is necessarily a
A parallelogram having unequal adjacent
sides and equal diagonals is necessarily a
rectangle.
Side of a square garden is 30 m. If the scale used to draw its picture is 1 cm : 5 m, the perimeter of the square is
Scale used
Side of square garden
Perimeter
ABD and BCD are isosceles triangles. Where AB = BC = BD. The special name that is given to quadrilateral ABCD is
In (isosceles triangle property)
In ,
(isosceles triangle property)
Also,
ABDC and AD not BC hence ABCD is a trapezium
Find the area of polygon ABCDEF, if AD = 18 cm, AQ = 14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm and FM, EP, QC, BN are perpendicular to diagonal AD
A rhombus and a square have the same base. If the diagonals of the rhombus measure 30 cm and 16 cm respectively. Find the area of the square.
Each side of the square = each side of rhombus