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

MathematicsGeneral ScienceMaharashtra Board Solutions

**Exercise 35:**

**Solution 1:**

- The name of the quadrilateral is LMNP.
- The names of the vertices of the quadrilateral are L, M, N, P.
- The names of the angles of the quadrilateral using three letters are ∠LMN, ∠MNP, ∠NPL, ∠PLM.
- The names of the pairs of opposite sides of the quadrilateral are MN and LP, LM and PN.
- 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.
- The names of the pairs of the opposite angles of the quadrilateral are ∠LMN and ∠NPL, ∠PLM and ∠MNP.
- The names of the pairs of adjacent angles of the quadrilateral are ∠LMN and ∠MNP, ∠MNP and ∠NPL, ∠NPL and ∠PLM, ∠PLM and ∠LMN.
- The names of the diagonals of the quadrilateral are MP and LN.

**Exercise 36:**

**Solution 1:**

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

**Solution 2:**

**Solution 3:**

Given below is the quadrilateral with the given specifications:

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

**Exercise 37:**

**Solution 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° - 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°