Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3 Solutions
Complete Maharashtra State Board Balbharati & Yuvakbharati textbook solutions for Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3. Step-by-step solved exercises, numerical problems, and digest answers.
7 Solved Questions• 885 words
Practice Set 8.3 8th Std Maths Answers Chapter 8 Quadrilateral: Constructions and Types
Question 1Maharashtra Board Solution
Measures of opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of its each angle.
Solution & Step-by-Step Answer:
Let ₹PQRS be the parallelogram. m∠Q = (3x – 2)° and m∠S = (50 – x)° m∠Q = m∠S …..(i) [Opposite angles of a parallelogram are congruent] ∴ 3x – 2 = 50 – x ∴ 3x + x = 50 + 2 ∴ 4x = 52 ∴ x = ∴ x = 13 Now, m∠Q = (3x – 2)° = (3 x 13 – 2)° = (39 – 2)° = 37° ∴ m∠S = m∠Q = 37° …[From(i)] m∠P + m∠Q = 180° ….[Adjacent angles of a parallelogram are supplementary] ∴ m∠P + 37° = 180° ∴ m∠P = 180° – 37° = 143° ∴ m∠R = m∠P = 143° …..[Opposite angles of a parallelogram are congruent] ∴ The measures of the angles of the parallelogram are 37°, 143°, 37° and 143°.
Question 2Maharashtra Board Solution
Referring the given figure of a parallelogram, write the answers of questions given below. 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∠WZY = 120°, then m∠WXY = ? and m∠XWZ = ?
Solution & Step-by-Step Answer:
i. l(WZ) = 4.5 cm … [Given] l(X Y) = l(WZ) ….[Opposite sides of a parallelogram are congrument ] ∴ l(X Y) = 4.5cm
ii. l(YZ) = 8.2 cm …[Given] l(XW) = l(YZ) …[Opposite sides of a parallelogram are congruent] ∴ l(XW) = 8.2cm … [Given]
iii. l(OX) = 2.5 cm …[Given] l(OZ) = l(OX) ….[Diagonals of a parallelogram bisect each other] ∴ l(OZ) = 2.5cm
iv. l(WO) = 3.3 cm … [Given] l(WO) = l(WY) ….[Diagonals of a parallelogram bisect each other] ∴ 3.3 = l(WY) ∴ 3.3 x 2 = l(WY) ∴ l(WY) = 6.6cm
v. m∠WZY =120° … [Given] m∠WXY = m∠WZY …..[Opposite angles of a parallelogram are congrument] ∴ m∠WXY = 120° …(i) m∠XWZ + m∠WXY = 180° ….[Adjacent angles of a parallelogram are supplementary] ∴ m∠XWZ + 120° = 180° … [From (i)] ∴ m∠XWZ = 180°- 120° ∴ m∠XWZ = 60°
Question 3Maharashtra Board Solution
Construct a parallelogram ABCD such that l(BC) = 7 cm, m∠ABC = 40°, l(AB) = 3 cm
Solution & Step-by-Step Answer:
Opposite sides of a parallelogram are congruent. ∴ l(AB) = l(CD) = 3cm l(BC) = l(AD) = 7 cm
Question 4Maharashtra Board Solution
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 & Step-by-Step Answer:
Let ₹PQRS be the quadrilateral. Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4. Let the common multiple be x. ∴m∠P = x°, m∠Q = 2x°, m∠R = 3x° and m∠S = 4x° In ₹PQRS, m∠P + m∠Q + m∠R + m∠S = 360° …[Sum of the measures of the angles of a quadrilateral is 360°] ∴x° + 2x° + 3x° + 4x° = 360° ∴10 x° = 360° ∴x° = ∴x° = 36° ∴m∠P = x° = 36° m∠Q = 2x° = 2 × 36° = 72° m∠R = 3x° = 3 × 36° = 108° and m∠S = 4x° = 4 × 36° = 144° ∴The measures of the angles of the quadrilateral are 36°, 72°, 108°, 144°. Here, m∠P + m∠S = 36° + 144° = 180° Since, interior angles are supplementary, ∴side PQ || side SR m∠P + m∠Q = 36° + 72° = 108° ≠ 180° ∴side PS is not parallel to side QR. Since, one pair of opposite sides of the given quadrilateral is parallel. ∴The given quadrilateral is a trapezium.
Question 5Maharashtra Board Solution
Construct ₹BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
Solution & Step-by-Step Answer:
Question 6Maharashtra Board Solution
Construct ₹PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ₹PQRS is a parallelogram, which of the given information is unnecessary?
Solution & Step-by-Step Answer:
Maharashtra Board Class 8 Maths Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3 Intext Questions and Activities
Question 1Maharashtra Board Solution
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.
Solution & Step-by-Step Answer:
[Students should attempt the above activities on their own.]
Question 2. In the given figure of ₹ABCD, verify with a divider that seg AB ≅ seg CB and seg AD ≅ seg CD. Similarly measure ∠BAD and ∠BCD and verify that they are congruent. (Textbook pg. no. 48) Solution: [Students should attempt the above activities on their own.]