{"id":585446,"date":"2022-03-16T08:02:57","date_gmt":"2022-03-16T08:02:57","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=585446"},"modified":"2022-03-17T05:46:28","modified_gmt":"2022-03-17T05:46:28","slug":"maharashtra-board-solutions-class-8-maths-practice-set-8-3-chapter-8-quadrilateral-constructions-and-types","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/maharashtra-board-solutions-class-8-maths-practice-set-8-3-chapter-8-quadrilateral-constructions-and-types\/","title":{"rendered":"Maharashtra Board Solutions Class 8-Maths (Practice Set 8.3): Chapter 8- Quadrilateral: Constructions and Types"},"content":{"rendered":"\n

Class 8: Maths Chapter 8 solutions. Complete Class 8 Maths Chapter 8 Notes.<\/p>\n\n\n\n

Maharashtra Board Solutions Class 8-Maths (Practice Set 8.3): Chapter 8- Quadrilateral: Constructions and Types<\/h2>\n\n\n\n

Maharashtra Board 8th Maths Chapter 8, Class 8 Maths Chapter 8 solutions<\/p>\n\n\n\n

Question 1.
Measures of opposite angles of a parallelogram are (3x \u2013 2)\u00b0 and (50 \u2013 x)\u00b0. Find the measure of its each angle.
Solution:<\/strong>
Let \u20b9PQRS be the parallelogram.
m\u2220Q = (3x \u2013 2)\u00b0 and m\u2220S = (50 \u2013 x)\u00b0
\"Maharashtra
m\u2220Q = m\u2220S
\u2026..(i)
[Opposite angles of a parallelogram are congruent]
\u2234 3x \u2013 2 = 50 \u2013 x
\u2234 3x + x = 50 + 2
\u2234 4x = 52
\u2234 x = 524
\u2234 x = 13
Now, m\u2220Q = (3x \u2013 2)\u00b0
= (3 x 13 \u2013 2)\u00b0 = (39 \u2013 2)\u00b0 = 37\u00b0
\u2234 m\u2220S = m\u2220Q = 37\u00b0 \u2026[From(i)]
m\u2220P + m\u2220Q = 180\u00b0
\u2026.[Adjacent angles of a parallelogram are supplementary]
\u2234 m\u2220P + 37\u00b0 = 180\u00b0
\u2234 m\u2220P = 180\u00b0 \u2013 37\u00b0 = 143\u00b0
\u2234 m\u2220R = m\u2220P = 143\u00b0
\u2026..[Opposite angles of a parallelogram are congruent]
\u2234 The measures of the angles of the parallelogram are 37\u00b0, 143\u00b0, 37\u00b0 and 143\u00b0.<\/p>\n\n\n\n

Question 2.
Referring the given figure of a parallelogram, write the answers of questions given below.<\/strong>
i. If l(WZ) = 4.5 cm, then l(XY) = ?
ii. If l(YZ) = 8.2 cm, then l(XW) = ?
iii. If l(OX) = 2.5 cm, then l(OZ) = ?
iv. If l(WO) = 3.3 cm, then l(WY) = ?
v. If m\u2220WZY = 120\u00b0, then m\u2220WXY = ? and m\u2220XWZ = ?
\"Maharashtra
Solution:
<\/strong>i. l(WZ) = 4.5 cm \u2026 [Given]
l(X Y) = l(WZ) \u2026.[Opposite sides of a parallelogram are congrument ]
\u2234 l(X Y) = 4.5cm<\/p>\n\n\n\n

ii. l(YZ) = 8.2 cm \u2026[Given]
l(XW) = l(YZ)
\u2026[Opposite sides of a parallelogram are congruent]
\u2234 l(XW) = 8.2cm \u2026 [Given]<\/p>\n\n\n\n

iii. l(OX) = 2.5 cm \u2026[Given]
l(OZ) = l(OX)
\u2026.[Diagonals of a parallelogram bisect each other]
\u2234 l(OZ) = 2.5cm<\/p>\n\n\n\n

iv. l(WO) = 3.3 cm \u2026 [Given]
l(WO) = 12 l(WY)
\u2026.[Diagonals of a parallelogram bisect each other]
\u2234 3.3 = 12 l(WY)
\u2234 3.3 x 2 = l(WY)
\u2234 l(WY) = 6.6cm<\/p>\n\n\n\n

v. m\u2220WZY =120\u00b0 \u2026 [Given]
m\u2220WXY = m\u2220WZY
\u2026..[Opposite angles of a parallelogram are congrument]
\u2234 m\u2220WXY = 120\u00b0 \u2026(i)
m\u2220XWZ + m\u2220WXY = 180\u00b0
\u2026.[Adjacent angles of a parallelogram are supplementary]
\u2234 m\u2220XWZ + 120\u00b0 = 180\u00b0 \u2026 [From (i)]
\u2234 m\u2220XWZ = 180\u00b0- 120\u00b0
\u2234 m\u2220XWZ = 60\u00b0<\/p>\n\n\n\n

Question 3.
Construct a parallelogram ABCD such that l(BC) = 7 cm, m\u2220ABC = 40\u00b0, l(AB) = 3 cm
Solution:<\/strong>
\"Maharashtra
Opposite sides of a parallelogram are congruent.
\u2234 l(AB) = l(CD) = 3cm
l(BC) = l(AD) = 7 cm
\"Maharashtra<\/p>\n\n\n\n

Question 4.
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4. Find the measure of its each angle. Write with reason, what type of a quadrilateral it is.
Solution:<\/strong>
Let \u20b9PQRS be the quadrilateral.
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4.
Let the common multiple be x.
\u2234m\u2220P = x\u00b0, m\u2220Q = 2x\u00b0, m\u2220R = 3x\u00b0 and m\u2220S = 4x\u00b0
In \u20b9PQRS,
m\u2220P + m\u2220Q + m\u2220R + m\u2220S = 360\u00b0
\u2026[Sum of the measures of the angles of a quadrilateral is 360\u00b0]
\u2234x\u00b0 + 2x\u00b0 + 3x\u00b0 + 4x\u00b0 = 360\u00b0
\u223410 x\u00b0 = 360\u00b0
\u2234x\u00b0 = 36010
\u2234x\u00b0 = 36\u00b0
\u2234m\u2220P = x\u00b0 = 36\u00b0
\"Maharashtra
m\u2220Q = 2x\u00b0 = 2 \u00d7 36\u00b0 = 72\u00b0
m\u2220R = 3x\u00b0 = 3 \u00d7 36\u00b0 = 108\u00b0 and
m\u2220S = 4x\u00b0 = 4 \u00d7 36\u00b0 = 144\u00b0
\u2234The measures of the angles of the quadrilateral are 36\u00b0, 72\u00b0, 108\u00b0, 144\u00b0.
Here, m\u2220P + m\u2220S = 36\u00b0 + 144\u00b0 = 180\u00b0
Since, interior angles are supplementary,
\u2234side PQ || side SR
m\u2220P + m\u2220Q = 36\u00b0 + 72\u00b0 = 108\u00b0 \u2260 180\u00b0
\u2234side PS is not parallel to side QR.
Since, one pair of opposite sides of the given quadrilateral is parallel.
\u2234The given quadrilateral is a trapezium.<\/p>\n\n\n\n

Question 5.
Construct \u20b9BARC such that
l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
Solution:<\/strong>
\"Maharashtra<\/p>\n\n\n\n

Question 6.
Construct \u20b9PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m\u2220Q = 110\u00b0, m\u2220R = 70\u00b0. If it is given that \u20b9PQRS is a parallelogram, which of the given information is unnecessary?
Solution:<\/strong>
\"Maharashtra<\/p>\n\n\n\n

  1. Since, the opposite sides of a parallelogram are congruent.
    \u2234 Either l(PQ) or l(SR) is required.<\/li>
  2. To construct a parallelogram lengths of adjacent sides and measure of one angle is required.
    \u2234 Either l(PQ) and m\u2220Q or l(SR) and m\u2220R is the unnecessary information given in the question.<\/li><\/ol>\n\n\n\n

    Intext Questions and Activities<\/strong><\/p>\n\n\n\n

    Question 1.
    Draw a parallelogram PQRS. Take two rulers of different widths, place one ruler horizontally and draw lines along its edges. Now place the other ruler in slant position over the lines drawn and draw lines along its edges. We get a parallelogram. Draw the diagonals of it and name the point of intersection as T.<\/strong><\/p>\n\n\n\n

    1. Measure the opposite angles of the parallelogram.<\/li>
    2. Measure the lengths of opposite sides.<\/li>
    3. Measure the lengths of diagonals.<\/li>
    4. Measure the lengths of parts of the diagonals made by point T. (Textbook pg. no. 47)<\/li><\/ol>\n\n\n\n
      \"Maharashtra<\/figure>\n\n\n\n

      Solution:
      <\/strong>[Students should attempt the above activities on their own.]<\/p>\n\n\n\n

      Question 2.
      In the given figure of \u20b9ABCD, verify with a divider that seg AB \u2245 seg CB and seg AD \u2245 seg CD. Similarly measure \u2220BAD and \u2220BCD and verify that they are congruent. (Textbook pg. no. 48)
      \"Maharashtra
      Solution:<\/strong>
      [Students should attempt the above activities on their own.]<\/p>\n\n\n\n

      Download PDF<\/strong><\/h2>\n\n\n\n

      Maharashtra Board Solutions Class 8-Maths (Practice Set 8.3): Chapter 8- Quadrilateral: Constructions and Types<\/p>\n\n\n\n

      Download PDF<\/strong>: Maharashtra Board Solutions Class 8-Maths (Practice Set 8.3): Chapter 8- Quadrilateral: Constructions and Types PDF<\/a><\/p>\n\n\n\n

      Chapterwise Maharashtra Board Solutions Class 8 Maths :<\/strong><\/h2>\n\n\n\n