Question

Questions :

1)Is quadrilateral ABCD a parallelogram,it’s angle A =70 Degrees and angle C =65 degrees ? Give reasons

2)BASE is a rectangle.its diagonals intersect at O . Find x , if OB = 5x +1 and OE = 2x+ 4

Answer 1

Answer:

1)

Quadrilateral ABCD is not a parallelogram.

Step-by-step explanation:

In a parallelogram, the opposite angles must be equal.

So, if ABCD is indeed a parallelogram, then angle A and angle C being opposite angles must be equal.

However, as stated in question, angle A = 70 degrees

and angle C = 65 degrees.

Thus angle A and angle C are not equal.

Hence, the condition that opposite angles must be equal is not met. Hence there is a contradiction to our assumption. Hence, quadrilateral ABCD is not a parallelogram.

2)

   We know that in rectangle, length of both the diagonals remains same.

So, { from the given diagram }

Length of 1st diagonal = Length of 2nd diagonal

Length of AE = length of BS

{ From the diagram, AE = 2x + 4 and BS = 5x + 1 {

2x + 4 = 5x + 1 4 - 1 = 5x - 2x

3 = 3x

3/3  = x

1 = x

Therefore the value of x satisfying the length of diagonals of rectangle BASE is 1 .