Question

In the adjoining figure, ABCD is a parallelogram and
ZA = 56°. Find the values of x, y, z and w.
​

Answer 1

Answer:

x=124°, y=56°, z=124°, w=56°

1. x+angle A=180° [adjacent sides are supplementary in parallelogram ]
2. x=180°-56°
3. x=124°
4. angle A=y [opposite angle are equal in parallelogram ]
5. z=x=124° [opposite angle are equal in parallelogram ]
6. z+w=180°[linear pair ]
7. w=180°-124°
8. w=56°
9. Hence, the value of x,y,z and w=124°,56°,124°,56°respectively.

Answer 2

Correct question -:

In the adjoining figure, ABCD is a parallelogram and ∠A = 56°. Find the values of x, y, z and w.

Answer -:

• ∠x = 124

• ∠y is 56

• ∠z = 124

• ∠w = 56

Explanation -:

Given :

• Adjoining figure, ABCD is a parallelogram and
• ZA = 56°

To Find :

• The values of x, y, z and w.

Solution :

1)Opposite angles of a parallelogram are equal.

So,

∠A = ∠y

56 = 56

Therefore ∠y is 56

2) ∠A & ∠x are supplementary angles because these interior angles lies on same side of the transversal. In the same way, ∠B & ∠C are supplementary angles.

So,

Therefore,

∠A + ∠x = 180

56 + ∠x = 180

∠x = 124

Therefore,∠x = 124

3)Opposite angles of a parallelogram are equal.

So,

∠D= ∠z

124 = 124

Therefore,∠z = 124

4)We know ∠z is 124 and ∠B is 180.

So,

∠z +∠w =∠B  [By angle sum property]

124 +∠w = 180

∠w = 180 - 124

∠w = 56

Property of parallelogram :-

• The opposite sides are congruent.

• The opposite angles are congruent.

• The consecutive angles are supplementary.

• If anyone of the angles is a right angle, then all the other angles will be right.

• The two diagonals bisect each other.

• Each diagonal bisects the parallelogram into two congruent triangles.

• The diagonals separate it into congruent.

(Figure in attachment)