Question

Construct a quadrilateral \[PQRS\] such that \[PQ = 3.5cm\], \[QR = 4.5cm\], \[RS = 4cm\], \[\angle Q = 110^\circ \] and \[\angle R = 80^\circ \]. Then \[m\angle P\] (in deg.) is equal to:

Answer 1

Hint:
Here we need to construct the quadrilateral of the given sides and the angles. We will first draw the base of the quadrilateral and then we will draw the angles at both the ends of the base of the quadrilateral and then we will cut the length of the other two sides of the quadrilateral using the compass and use all the information given in the question to draw the quadrilateral and at last we will measure required angle asked in the question.

Complete step by step solution:
Here we need to construct the quadrilateral of the given sides and the angles.
It is given that \[PQRS\] is a quadrilateral and \[PQ = 3.5cm\], \[QR = 4.5cm\], \[RS = 4cm\], \[\angle Q = 110^\circ \] and \[\angle R = 80^\circ \].
Now, we will first draw the line segment \[QR\] of length \[4.5cm\]

Now, we will draw the angle \[\angle R = 80^\circ \] and \[\angle Q = 110^\circ \] using the protector.

Now, we will stretch the two ends of the compass to the length of \[3.5cm\] and then we will consider the point \[Q\] as the center and draw an arc using the compass and we will mark that point to be point \[P\]. Similarly, we will stretch the two ends of the compass to the length of \[4cm\] and then we will consider the point \[R\] as the center and draw an arc using the compass and we will mark that point to be point \[S\]

Now, we will join the points \[PS\].

Now, we will measure the angle \[P\] using the protector and we will find that the \[\angle P = 78^\circ \].

Note:
Here we have obtained the missing angle of the quadrilateral. A quadrilateral is defined as a plane figure or a two dimensional figure that has four edges or sides, and also it has four corners or vertices. Some examples of the quadrilateral are square, rectangle, rhombus, etc. Measures of all the angles of a square, rectangle, and rhombus are \[90^\circ \].