8th Maths 3.3

Exercise 3.3

Q1. Given a parallelogram

$text{ABCD}$ . Complete each statement with the definition or property used.

$text{AD}$ = ..........

ii)

$angle text{DCB}$ = ............

iii)

$text{OC}$ = ...........

iv)

$m angle text{DAB} + m angletext{CDA}$ = ..........

$text{Answer:}$

$text{BC (Opposite sides are equal)}$

ii)

$angletext{DAB (Opposite angles are equal)}$

iii)

$text{OA (Diagonals bisect each other)}$

iv)

$180^circ text{(Interior opposite angles,}overline text{AB}∥ overline text{DC})$

Q2. Consider the following parallelograms. Find the values of the unknowns

$text{x, y, z}$

$text{Sol.}$

$angle text{B} + angle text{C} = 180^circ text{ [adjacent angles]}$

$100^circ + text{x} = 180^circ$

$text{x} = 180^circ - 100^circ$

$text{x} = 80^circ$

$angle text{D} = angle text{B} text{ [opposite angles]}$

$text{y} = 100^circ$

$angle text{A} = angle text{C} text{ [opposite angles]}$

$text{z = x}$

$text{z} = 80^circ$

$text{Answer:}$

$text{x} = 80^circ, text{y} = 100^circ, text{z} = 80^circ$

ii)

$text{Sol.}$

$50^circ + text{x} = 180^circ text{ [adjacent angles]}$

$text{x} = 180^circ - 50^circ$

$text{x} = 130^circ$

$text{y = x [ opposite angles]}$

$text{y} = 130^circ$

$text{z = x [corresponding angles]}$

$text{z} = 130^circ$

$text{Answer:}$

$text{x} = 130^circ, text{y} = 130^circ, text{z} = 130^circ$

iii)

$text{Sol.}$

$text{x} = 90^circ text{ [vertically opposite angles]}$

$text{angle sum property of triangle}$

$text{x + y + } 30^circ = 180^circ$

$90^circ + text{y} + 30^circ = 180^circ$

$text{y} + 120^circ = 180^circ$

$text{y} = 180^circ - 120^circ$

$text{y} = 60^circ$

$text{z = y [alternate angles]}$

$text{z} = 60^circ$

$text{Answer:}$

$text{x} = 90^circ, text{y} = 60^circ, text{z} = 60^circ$

iv)

$text{Sol.}$

$text{x} + 80^circ = 180^circ text{ [adjacent angles]}$

$text{x} = 180^circ - 80^circ$

$text{x} = 100^circ$

$text{y} = 80^circ text{ [opposite angles]}$

$text{z} = 80^circ text{ [ corresponding angles]}$

$text{Answer:}$

$text{x} = 100^circ, text{y} = 80^circ, text{z} = 80^circ$

$text{Sol.}$

$text{y} = 112^circ text{ [opposite angles]}$

$text{angle sum property of triangle}$

$text{x + y + }40^circ = 180^circ$

$text{x} + 112^circ + 40^circ = 180^circ$

$text{x} + 152^circ = 180^circ$

$text{x} = 180^circ - 152^circ$

$text{x} = 28^circ$

$text{z = x [alternate angles]}$

$text{z} = 28^circ$

$text{Answer:}$

$text{x} = 28^circ, text{y} = 112^circ, text{z} = 28^circ$

Q3. Can a quadrilateral

$text{ABCD}$ be a parallelogram if

$angletext{D} + angletext{B} = 180^circ$ ?

$text{Sol.}$

$text{Answer:}$

$text{Can be but need not be}.$

ii)

$text{AB = DC = 8 cm, AD = 4 cm }$ and

$text{BC = 4.4 cm}$ ?

$text{Sol.}$

$text{In a parallelogram, opposite sides are equal,}$

$text{but here AD}ne text{BC}.$

$text{Answer:}$

$text{No}$ .

iii)

$angle text{A =70}^circ$ and

$angle text{C = 65}^circ$ ?

$text{Sol.}$

$text{In a parallelogram, opposite angles are equal, }$

$text{but here, }angle text{A}ne angle text{C}.$

$text{Answer:}$

$text{No.}$

Q4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

$text{Sol.}$

$text{Answer:}$

$text{A kite, for example.}$

Q5. The measures of two adjacent angles of a parallelogram are in the ratio

$3 : 2$ . Find the measure of each of the angles of the parallelogram.

$text{Sol.}$

$text{Let first angle is 3x}$

$text{and second angle is 2x}$

$text{Sum of two adjacent angles of a}$

$text{parallelogram are 180}^circ$

$text{3x + 2x = }180^circ$

$text{5x} = 180^circ$

$text{x} = 180^circ/5$

$text{x} = 36^circ$

$text{3x =} 3times36^circ = 108^circ$

$text{2x =} 2times36^circ = 72^circ$

$text{Answer:}$

$108^circ, 72^circ$ .

Q6.Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

$text{Sol.}$

$text{Let first angle is x}$

$text{and second angle is x}$

$text{Sum of two adjacent angles of a}$

$text{parallelogram are 180}^circ$

$text{x + x =}180^circ$

$text{2x} = 180^circ$

$text{x} = 180^circ/2$

$text{x} = 90^circ$

$text{Each angle measures }90^circ$

$text{Answer:}$

$text{Each is a right angle.}$

Q7. The adjacent figure

$text{HOPE}$ is a parallelogram. Find the angle measures

$x, y,$ and

$z$ . State the properties you use to find them.

$text{Sol.}$

$angle text{EHO =}70^circ text{[Corresponding angles]}$

$70^circ + text{x} =180^circ text{[adjacent angles]}$

$text{x}= 180^circ - 70^circ$

$text{x}= 110^circ$

$text{y}= angle text{EHO [alternate angles]}$

$text{y} = 40^circ$

$angle text{EHO = }70^circ text{[Corresponding angles]}$

$angle text{EOP }+ angle text{PHO =}70^circ$

$40^circ + z = 70^circ$

$z = 70^circ - 40^circ$

$z = 30^circ$

$text{Answer:}$

$text{x} = 110^circ, text{y} = 40^circ, text{z} = 30^circ$ .

Q8. The following figures

$text{GUNS}$ and

$text{RUNS}$ are parallelograms.

Find

$x$ and

$y$ . (Lengths are in cm)

$text{Sol.}$

$text{GUNS}$

$text{3x = 18 [opposite sides of parallelogram]}$

$text{x} =18/3$

$text{x} = 6$

$text{3y - 1 = 26 [opposite sides of parallelogram]}$

$text{3y = 26 + 1}$

$text{y} = 27/3$

$text{y} = 9$

$text{Answer:}$

$text{x = 6, y = 9}$

$text{Sol.}$

$text{RUNS}$

$text{The diagonals of a parallelogram bisect}$

$text{each other}$

$text{y + 7 = 20}$

$text{y = 20 - 7}$

$text{y = 13}$

$text{and}$

$text{x + y = 16}$

$text{x + 13 = 16}$

$text{x = 16 - 13}$

$text{x = 3}$

$text{Answer:}$

$text{x = 3, y = 13}$

Q9. In the above figure both

$text{RISK}$ and

$text{CLUE}$ are parallelograms. Find the value of

$x$ .

$text{Sol.}$

$text{RISK}$

$angle text{K} + angle text{S} = 180^circ text{[adjacent angles]}$

$120^circ + angle text{S} = 180^circ$

$angle text{S} = 180^circ - 120^circ$

$angle text{S} = 60^circ$

$text{and}$

$text{CLUE}$

$angle text{E} = angle text{L [opposite angles]}$

$angle text{E} = 70^circ$

$text{Now}$

$text{Angle sum property of triangle}$

$text{x}+ 70^circ + 60^circ = 180^circ$

$text{x}+ 130^circ = 180^circ$

$text{x} = 180^circ - 130^circ$

$text{x} = 50^circ$

$text{Answer:}$

$text{x} = 50^circ$ .

Q10. Explain how this figure is a trapezium. Which of its sides are parallel? (Fig.)

$text{Sol.}$

$text{Answer:}$

$overline text{NM}∥ overline text{KL} text{ (sum of interior opposite}$

$text{ angles is}$

$180^circ).$

$text{So, KLMN is a trapezium.}$

Q11. Find

$m angletext{C}$ in Fig. if

$overline text{AB} ∥ overline text{DC}$ .

$text{Sol.}$

$angle text{B} + angle text{C} = 180^circ [ overline text{AB}∥ overline text{DC}]$

$120^circ + angle text{C} = 180^circ$

$angle text{C} = 180^circ - 120^circ$

$angle text{C} = 60^circ$

$text{Answer:}$

$60^circ$ .

Q12. Find the measure of

$angletext{P}$ and

$angle text{S}$ if

$overline text{SP} ∥ overline text{RQ}$ in Fig. (If you find

$mangle text{R}$ , is there more than one method to find

$mangletext{P}$ ?)

$text{Sol.}$

$angle text{P} + angle text{Q} = 180^circ [overline text{SP} ∥ overline text{RQ}]$

$angle text{P} + 130^circ = 180^circ$

$angle text{P} = 180^circ - 130^circ$

$angle text{P} = 50^circ$

$text{and}$

$angle text{S} + angle text{R} = 180^circ [overline{SP}∥ overline text{RQ}]$

$angle text{S} + 90^circ = 180^circ$

$angle text{S} = 180^circ - 90^circ$

$angle text{S} = 90^circ$

$text{Answer:}$

$angle text{P} = 50^circ, angle text{S} = 90^circ$ .

Search This Blog

8th Maths 3.3

NCERT Class 8th solution of exercise 3.1

NCERT Class 8th solution of Exercise 3.2

NCERT Class 8th solution of Exercise 3.4

Exercise 3.3

Comments

Popular posts from this blog

10th Maths Chapter 1

CBSE 10th and 12th Result

RSKMP 5th & 8th Result