The sum of the interior angles of a polygon is four times the sum of its exterior angles. Find
the number of sides in the polygon.
The angles of a pentagon are in the ratio 4:8:6:4:5. Find each angle of the pentagon.
One angle of a six-sided polygon is 1400 and the other angles are equal. Find the measure of
each equal angle.
In a polygon, there are 5 right angles and the remaining angles are equal to 1950 each. Find
\text { Three angles of a seven sided polygon are } 132^{0} \text { each and the remaining four angles are } equal. Find the value of each equal angle.
\text { Two angles of an eight sided polygon are } 142^{0} \text { and } 176^{\circ} \text { . }If the remaining angles are equal
to each other; find the magnitude of each of the equal angles.
In a pentagon ABCDE, AB is parallel to DC and angles A: E: D=3:4:5. Find angle E.
AB, BC, and CD are the three consecutive sides of a regular polygon. If ∠BAC=15° ;
Find,
(i) Each interior angle of the polygon.
(ii) Each exterior angle of the polygon.
(iii) The number of sides of the polygon.
The ratio between an exterior angle and an interior angle of a regular polygon is 2:3. Find
The difference between an exterior angle of (n-1) sided regular polygon and an exterior
the angle of (n+2) sided regular polygon is 6^{0} . \text { Find the value of } \mathbf{n}
Two alternate sides of a regular polygon, when produced, meet at a right angle. Find:
(i) The value of each exterior angle of the polygon.
(ii) The number of sides in the polygon.
State, ‘true’ or ‘false’
If the diagonals of a quadrilateral bisect each other at a right angle, the quadrilateral
is a square.
The diagonals of a quadrilateral bisect each other.
Each diagonal of a rhombus bisects it.
The quadrilateral, whose four sides are equal, is a square.
The diagonals of a rectangle bisect each other.
Every parallelogram is a rhombus.
The diagonals of a rhombus are equal.
If two adjacent sides of a parallelogram are equal, it is a rhombus.
In the figure given below, AM bisects angle A and DM bisects angle D of parallelogram ABCD. Prove that: ; \angle \mathbf{A M D}=90^{\circ}
In the following figure, AE and BC are equal and parallel and the three sides AB, CD and
DE is equal to one another. If angle\text { A is } 102^{0}, \text { find the angles } A E C \text { ad } B C D \text { . }
In a square ABCD, diagonals meet at O. P is a point on BC, such that OB=BP.
Show that:
The given figure shows a square ABCD and an equilateral triangle ABP.
Calculate:
(i) ∠AOB
(ii) ∠BPC
(iii) ∠PCD
(iv) Reflex ∠APC
Every rhombus is a parallelogram.
If DEC is an equilateral triangle, calculate:
(i) ∠CBE
(ii) ∠DBE
Find the value of x and y.
The angles of a quadrilateral are in the ratio 3:4:5:6. Show that the quadrilateral is a
trapezium.
In a parallelogram ABCD, AB=20 cm and AD=12cm. The bisector of angle A meets DC at
E nd BC produced at F. Find the length of CF.
In parallelogram ABCD, AP and AQ are perpendiculars from the vertex of obtuse angle A as
shown. If angles x:y=2:1; find the angles of the parallelogram.
E is the mid-point of sides AB and F is the midpoint of side DC pf parallelogram ABCD. Prove
that AEFD is a parallelogram.
The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a
rhombus.
The given figure shows a parallelogram ABCD in which AE=EF=FC. Prove that:
(i) DE is parallel to FB
(ii) DE=FB
(iii) DEBF is a parallelogram.
In the given figure, ABCD is a parallelogram in which AP bisects angle A and BQ bisects
angle B. Prove that:
(i) AQ = BP
(ii) PQ = CD
(iii) ABPQ is a parallelogram
In the given figure, ABCD is a parallelogram. Prove that: AB = 2BC.
Prove that the bisectors of opposite angles of a parallelogram are parallel.
Prove that the bisectors of interior angles of a parallelogram form a rectangle.
Prove that the bisectors of the interior angles of a rectangle form a square.
In parallelogram ABCD, the bisector of angle A meets DC at P and AB=2AD.
Prove that:
(i) BP bisects angle B.
\text { (ii) Angle } A P B=90^{\circ}
Points M and N are taken on the diagonal AC of a parallelogram ABCD such that
AM=CN. Prove that BMDN is a parallelogram.
In the following figure, ABCD is a parallelogram. Prove that:
(i) AP bisects angle A
(ii) BP bisects angle B
(iii) Angle DAP + Angle CBP = Angle APB
ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If
AP=DQ; prove that AP and DQ are perpendicular to each other.
In a quadrilateral ABCD, AB=AD and CB=CD. Prove that:
(i) AC bisects angle BAD.
(ii) AC is a perpendicular bisector of BD.
The following figure shows a trapezium ABCD in which AB is parallel to DC and AD=BC.
In the given figure, AP is the bisector of ∠A and CQ is the bisector of ∠C of a parallelogram
ABCD. Prove that APCQ is a parallelogram.
In case of a parallelogram, prove that:
(i) The bisector of any two adjacent angles intersect at 900.
(ii) The bisectors of opposite angles are parallel to each other.
The diagonals of a rectangle intersect each other at right angles, prove that the rectangle is
a square.
In the following figure, ABCD and PQRS are two parallelograms such that \angle D=120^{\circ} \text { and } \angle Q=70^{\circ} . \text { Find the value of } x
In the following figure, ABCD is a rhombus and DCFE is a square.
If ∠ABC=560, find:
(i) ∠DAE
(ii) ∠FEA
(iii) ∠EAC
(iv) ∠AEC
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