Answer: Option C. -> Using 2 angles
:
C
Suppose, we need to construct a triangle of whose two given sides are 'a' cm and 'b' cm and three given angles are x, y and z.

Step 1:Draw PQ= acm.
Step 2: Construct angle measuring x° at point Q.
Step 3: with Q as centre and radius equal to b cm cut an arc to meet at R.
Step 4: Construct an angle measuring y° at point R.
Step 5: Construct an angle measuring z° at P.
Step 6: The point of intersection of both thelines is the required point. Let this point beS.
Thus, fourth point is plotted using lines made by any two angles.

Answer: Option B. -> 2
:
B

2 triangles are needed to construct a quadrilateral. The triangles will have thediagonal as common side.

Answer: Option A. -> SSS
:
A
A quadrilateral is made up of two triangles. Diagonal is the common side for both the triangles. If all the four sides and a diagonal is known, then we can construct a quadrilateral by constructing two triangles. The two triangles are constructed using SSS property.

Answer: Option D. -> 4
:
D

Consider quadrilateral ABCD above. The triangles that can be constructed with diagonals are the following- ABC, DBC, BAD, CAD. Hence, 4 triangles are possible.

Answer: Option D. -> Infinite
:
D

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.

Answer: Option B. -> Trapezium
:
B
The given is 3 sides and 2 included angles
$⟹$ The angles are adjacent angles
Also their sum is${75}^{\circ }+{105}^{\circ }={180}^{\circ }$
$⟹$ Given angles are supplementary.
Then the remaining two angles are alsosupplementary. [$\because$ Sum of all the angles of a quadrilateral is ${360}^0$]
Hence, the quadrilateral is a trapezium as in a trapeziumadjacent angles are supplementary angles and since its given no sides are equal , it cannot be a parallelogram( opposite sides are equal) and square, rhombus( all sides are equal)

Answer: Option C. -> Using 2 angles
:
C

Suppose, we need to construct a triangle of whose two given sides are 'a' cm and 'b' cm and three given angles are x, y and z.

 
Step 1: Draw PQ = a cm.
Step 2: Construct angle measuring x° at point Q.
Step 3: with Q as centre and radius equal to b cm cut an arc to meet at R.
Step 4: Construct an angle measuring y° at point R.
Step 5: Construct an angle measuring z° at P.
Step 6: The point of intersection of both the lines is the required point. Let this point be S. 
Thus, fourth point is plotted using lines made by any two angles.

Answer: Option B. -> Trapezium
:
B

The given is 3 sides and 2 included angles
$⟹$ The angles are adjacent angles
Also their sum is ${75}^{\circ }+{105}^{\circ }={180}^{\circ }$
$⟹$ Given angles are supplementary.
Then the remaining two angles are also supplementary.  [$\because$ Sum of all the angles of a quadrilateral is ${360}^0$]
Hence, the quadrilateral is a trapezium as in a trapezium  adjacent angles are supplementary angles and since its given no sides are equal , it cannot be a parallelogram( opposite sides are equal) and square, rhombus( all sides are equal)

Answer: Option B. -> 2
:
B

2 triangles are needed to construct a quadrilateral. The triangles will have the diagonal as common side.

Answer: Option D. -> Infinite
:
D

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.