Question

In the given figure, ABCF is a parallelogram, DME,
DGB and DFC are straight lines. The measure of
ZADG - ZMDF is
72°CE
520c
(1) 14
(2) 5°
(3) 16°
(4) 12°​

Answer 1

Answer:

Given data:

ABCF is a parallelogram

Angle DAF = 56°

Angle GBE = 90°

Angle MEB = 72°

Angle FCE = 52°

To find: the measure of [Angle ADG – angle MDF]

Solution:

Step 1:

∠BGA = ∠GBE = 90° ….. [alternate interior angles] ….. (i)

Since the exterior angles of a triangle is equal to the sum of opposite interior angles.

So, considering ∆ ADG,

∴ ∠BGA = ∠DAG + ∠ADG

⇒ 90° = 56° + ∠ADG ….. [substituting value from (i) and ∠DAF = ∠DAG]

⇒ ∠ADG = 34° ….. (ii)

Step 2:

∠CEM = 180° – ∠MEB ….. [linear pairs]  

⇒∠CEM = 180° – 72° = 108°

Step 3:

In ∆ DEC, applying the angle sum property,

∠CED + ∠DCE + ∠EDC = 180°

⇒ ∠CEM + ∠FCE + ∠EDC = 180°

⇒ ∠EDC = 180° - [108°+52°] = 20° = ∠MDF….. (iii)

Step 4:

Thus, from (ii) & (iii), we get

∠ADG – ∠MDF

= 34° - 20°

= 14°