Question

5. Can a quadrilateral ABCD be a parallelogram, give reasons in support of your answer."
1) ZA + 2C = 180°?
60 AD = BC = 6 cm, AB = 5 cm, DC = 4.5 cm?
(ZD ZB = 80°, ZD = 70°?
(iv) ZB + ZC = 180°?
fo) AC = BD?​

Z stands for angle

Answer 1

Answer:

. quadrilaterals 3

Solution: Here, `x = 180° - 100° = 80°`

As opposite angles are equal in a parallelogram

So, `y = 100°` and `z = 80°`

(ii)

quadrilaterals 5

Solution: x, y and z will be complementary to 50°.

So, Required angle `= 180° - 50° = 130°`

(iii)

quadrilaterals 6

Solution: z being opposite angle= 80°

x and y are complementary, x and y

`= 180° - 80° = 100°`

(iv)

quadrilaterals 7

Solution: As angles on one side of a line are always complementary

So, `x = 90°`

So, `y = 180° - (90° + 30°) = 60°`

The top vertex angle of the above figure `= 60° xx 2=120°`

Hence, bottom vertex Angle = 120° and

`z = 60°`

(v)

quadrilaterals 8

Solution: y= 112°, as opposite angles are equal in a parallelogram

As adjacent angles are complementary so angle of the bottom left vertex

`=180°-112°=68°`

So, `z=68°-40°=28°`

Another way of solving this is as follows:

As angles x and z are alternate angles of a transversal so they are equal in measurement.

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.