Question

The following figure shows a quadrilateral in
which sides AB and DC are parallel.
If ZA: ZD = 4:5, ZB = (3x - 15)
and ZC = (4x + 20), find each angle of the
quadrilateral ABCD.
​

Answer 1

Answer:

ZA = 80°

ZB = 60°

ZC = 120°

ZD = 100°, where Z = Angle.

Step-by-step explanation:

As we know that sum of corresponding angle in parallelogram is 180°.

Here ZA, ZD are corresponding angle. ZC and ZB are also corresponding angle.

So, according to question

ZC + ZB = 180°

=> (4x + 20)° + (3x - 15)° = 180°

=> 7x + 5° = 180°

=> x = 25° ( after solving).

So, ZC = 120° and ZB = 60°.

As given in question, ZA : ZD = 4 : 5

So, 4y + 5y = 180° (Sum of corresponding angle is 180°)

=> 9y = 180°

=> y = 20°

So, ZA = 80° and ZD = 100°.

Here, Z = angle.