Some figures are given below.
Classify each of them on the basis of the following:
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
Find the sum of measures of all interior angles of a polygon with the number of
sides:
(i) 8
(ii) 12
Find the number of sides of a regular polygon whose each exterior angles has a measure of
(i) 24^{\circ} (ii) 60^{\circ} (iii) 72 ^{\circ}
Find the number of sides of a regular polygon if each of its interior angles is
(i) 90^{\circ} (ii) 108^{\circ} (iii) 165^{\circ}
Find the number of sides in a polygon if the sum of its interior angles is:
(i) 1260^{\circ} (ii) 1980^{\circ} (iii) 3420^{\circ}
If the angles of a pentagon are in the ratio 7 : 8 : 11 : 13 : 15, find the angles.
The angles of a pentagon are x^{\circ},(x-10)^{\circ},(x+20)^{\circ},(2 x-44)^{\circ} \text { and }(2 x-70)^{\circ}
The exterior angles of a pentagon are in ratio 1 : 2 : 3 : 4 : 5. Find all the interior angles of the pentagon.
In a quadrilateral ABCD, AB || DC. If ∠A : ∠D = 2:3 and ∠B : ∠C = ∠7 : 8, find the measure of each angle.
From the adjoining figure, find
(i) x
(ii) ∠DAB
(iii) ∠ADB
Find the angle measure x in the following figures
(i) In the given figure, find x + y + z.
A heptagon has three equal angles each of 120 and four equal angles. Find the
size of equal angles.
The ratio between an exterior angle and the interior angle of a regular polygon is 1
: 5. Find
(i) the measure of each exterior angle
(ii) the measure of each interior angle
(iii) the number of sides in the polygon
Each interior angle of a regular polygon is double of its exterior angle. Find the
number of sides in the polygon
In the given figure, ABCD is a parallelogram. Complete each statement along with
the definition or property used.
(i) AD = ………..
(ii) DC = ………..
(iii) ∠DCB = ………..
(iv) ∠ADC = ………..
(v) ∠DAB = ………..
(vi) OC = ………..
(vii) OB = ………..
(viii) m∠DAB + m∠CDA = ………..
Consider the following parallelograms. Find the values of x, y, z in each.
(i)
Two adjacent sides of a parallelogram are in the ratio 5 : 7. If the perimeter of a
parallelogram is 72 cm, find the length of its sides.
The measure of two adjacent angles of a parallelogram is in the ratio 4: 5. Find the
measure of each angle of the parallelogram.
Can a quadrilateral ABCD be a parallelogram, give reasons in support of your
answer.
(i) ∠A + ∠C= 180o?
(ii) AD = BC = 6 cm, AB = 5 cm, DC = 4.5 cm?
(iii) ∠B = 80o, ∠D = 70o?
(iv) ∠B + ∠C= 180o?
In the following figures, HOPE and ROPE are parallelograms. Find the measures of
angles x, y and z. State the properties you use to find them.
,
In the given figure TURN and BURN are parallelograms. Find the measures of x and y
(lengths are in cm).
In the following figure, both ABCD and PQRS are parallelograms. Find the value of x.
In the given figure, ABCD, is a parallelogram and diagonals intersect at O. Find :
(i) ∠CAD
(ii) ∠ACD
(iii) ∠ADC
In the given figure, ABCD is a parallelogram. Perpendiculars DN and BP are drawn
on diagonal AC. Prove that:
(i) ΔDCN ≅ ΔBAP
(ii) AN = CP
In the given figure, ABC is a triangle. Through A, B, and C lines are drawn parallel to
BC, CA, and AB respectively, which form a ΔPQR.
Show that 2(AB + BC + CA) = PQ + QR + RP
Identify all the quadrilaterals that have
(i) four sides of equal length
(ii) four right angles.
Explain how a square is
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Name the quadrilaterals whose diagonals
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
In the given figure, ABCD is a rhombus, find the values of x, y and z
In the given figure, ABCD is a trapezium. If ∠A : ∠D = 5 : 7, ∠B = (3x + 11)o and ∠C =
(5x – 31)o, then find all the angles of the trapezium.
In the given figure, ABCD is a rectangle. If ∠CEB : ∠ECB = 3 : 2 find
(i) ∠CEB,
(ii) ∠DCF
In the given figure, ABCD is a rectangle and diagonals intersect at O. If ∠AOB = 118o,
find
(i) ∠ABO
(ii) ∠ADO
(iii) ∠OCB
In the given figure, ABCD is a rhombus and ∠ABD = 50. Find :
(i) ∠CAB
(ii) ∠BCD
In the given isosceles trapezium ABCD, ∠C = 102. Find all the remaining angles of
the trapezium.
In the given figure, PQRS is a kite. Find the values of x and y.
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