Quadrilaterals – Maharashtra Board Class 7 Solutions for Mathematics

Quadrilaterals – Maharashtra Board Class 7 Solutions for Mathematics (English Medium)

MathematicsGeneral ScienceMaharashtra Board Solutions

Exercise 35:

Solution 1:

1. The name of the quadrilateral is LMNP.
2. The names of the vertices of the quadrilateral are L, M, N, P.
3. The names of the angles of the quadrilateral using three letters are ∠LMN, ∠MNP, ∠NPL, ∠PLM.
4. The names of the pairs of opposite sides of the quadrilateral are MN and LP, LM and PN.
5. The names of the pairs of the adjacent sides of the quadrilateral are MN and NP, NP and PL, PL and LM, LM and MN.
6. The names of the pairs of the opposite angles of the quadrilateral are ∠LMN and ∠NPL, ∠PLM and ∠MNP.
7. The names of the pairs of adjacent angles of the quadrilateral are ∠LMN and ∠MNP, ∠MNP and ∠NPL, ∠NPL and ∠PLM, ∠PLM and ∠LMN.
8. The names of the diagonals of the quadrilateral are MP and LN.

Exercise 36:

Solution 1:

1. Points in the interior of □STUV are A, B, and N.
2. Points in the exterior of □STUV are L and M.
3. Points on the quadrilateral are S, T, U, V, Q, P.

Solution 2:

Solution 3:

Given below is the quadrilateral with the given specifications:

1. Points in the interior: E and F.
2. Points in the exterior: N and T.
3. Points on the quadrilateral: U and V.

Exercise 37:

Solution 1:

1. The sum of the measures of the four angles of a quadrilateral is 360°.
   ∴ In □WXYZ, m∠W + m∠X + m∠Y + m∠Z = 360°
   ∴ 130° + 100° + m∠Y + 40° = 360°
   ∴ 270° + m∠Y = 360°
   ∴ m∠Y = 360° – 270° = 90°
2. The sum of the measures of the four angles of a quadrilateral is 360°.
   ∴ In □KLMN, m∠K + m∠L + m∠M + m∠N = 360°
   ∴ 90° + 90° + 90° + m∠N= 360°
   ∴ 270° + m∠N = 360°
   ∴ m∠N= 360° – 270° = 90°

Solution 2:

The sum of the measures of the four angles of a quadrilateral is 360°.
∴ In □PQRS, m∠P + m∠Q + m∠R + m∠S = 360°
∴ 70° + 115° + 75° + m∠S = 360°
∴ 260° + m∠S = 360°
∴ m∠S = 360° – 260° = 100°

Solution 3:

The sum of the measures of the four angles of a quadrilateral is 360°.
If one angle of the quadrilateral is 100°, then the sum of the remaining three angles of the quadrilateral
= 360° – 100°
= 260°