Question

Given that the quadrilateral shown is a parallelogram. Use the properties of parallelograms to find x if ∠A = 133° and ∠D = (3x + 35)°. A) x = 2 B) x = 4 C) x = 5 D) x = 7 2) Use the properties of parallelograms to find x if ∠A = 122° and ∠C = (2x + 60)°. A) x = 27 B) x = 29 C) x = 31 D) x = 33

Answer 1

(i) Option B , x=4

(ii) Option C, x=31

Explanation:

Step 1:

Angle properties of parallelogram is as follows :

- Opposite angles are equal

- Adjacent angles are supplementary, i.e the sum of the adjacent angles are 180

Step 2:

∠A and ∠D are adjacent and hence their sum is equal to 180

So, 133 + 3 x + 35 = 180

=> 3 x + 168 = 180

=> 3 x = 180-168 = 12

=> x = 4

Step 3:

∠A and ∠C are opposite and hence they are equal

So, 2 x + 60 = 122

2 x = 62

x = 31