Question

ABCD is a parallelogram in which ∠ADC=75∘ and side AB is produced to point E as shown in the figure. Find (x+y).

Answer 1

Step-by-step explanation:

Here, ∠C and ∠D are adjacent angles of the parallelogram

∴ ∠C + ∠D = 180°

⇒ x + 75° = 180°

⇒ x = 105°

Also, y = x = 105° [alt.int.angles]

Thus, x + y = 105° + 105° = 210°

Answer 2

Given:

ABCD is a parallelogram

∠ADC = 75°

Side AB is produced to point E.

To Find:

(x+ y)

Solution:

∠C and ∠D are adjacent angles of the parallelogram.

So, ∠C + ∠D = 180°

⇒ x + 75° = 180°

⇒ x = 180 - 75

⇒ x = 105°

Now,

y = x [alternate interior angles]

y = 105°

So,(x + y) = (105 + 105)

               = 210°

Therefore, (x+ y) = 210°.