Question

In quadrilateral ABCD, angleA: angleB:angleC:angleD = 3:4:6:7. Find all the angles of the quadrilateral.
Hence, prove that AB and DC are parallel. Is BC also parallel to AD?
plz ans it soon with diagram
as monday is my exam​

Answer 1

Answer:

Sum of Quadrilateral = 360°

3x + 4x + 6x + 7x = 360°

20x = 360°

x = 18°

★ Angles

3x = 3*18 = 54°

4x = 4*18 = 72°

6x = 6*18 = 108°

7x = 7*18 = 126°

• Now Prove

∠ IFH = 180 - 100 = 80° (linear pair)

∠ IHF = 180 - (80+45) = 180 - 125 = 55° (∠ sum property of  a traingle is 180 degrees)

thus, ∠ EGI and ∠ IHF are equal (both are 55°)

therefore, since alternate interior angles are equal the two lines AB and CD are parallel with GH transversal

Answer 2

Answer:

Quadrilateral = 360°

3x + 4x + 6x + 7x = 360°

20x = 360°

x = 18°

Now,

/_ = 180° - 100° = 80°

/_ = 180° - (80° + 45°) = 180° - 125° = 55°

Traingle = 180°

Both = 55°