Question

AB||CD and EF is a transversal intersecting AB and CD at P and Q respectively. If ∠APE = 7x - 10, ∠CQP = 4x + 11 and
∠DQF = 3y, then x + y = _______.

1. 20°
2. 18°
3. 26°
4. 39°

Answer 1

Hello Dear.

Here is the answer---


Refers to the attachment for the Answer.

From the Attachment, we can see that, 
∠ APE = ∠ CQP [Alternate Angles]
∴ 7x - 10 = 4x + 11
⇒ 7x - 4x = 11 + 10
⇒ 3x = 21
⇒ x = 7

Now, From the Attachment, we can see that,
∠CQP = ∠ DQF [Vertically Opposite angles]
∴ 4x + 11 = 3y
⇒ 4(7) + 11 = 3y
⇒ 3y = 28 + 11
⇒ 3y = 39
⇒ y = 13

Now,
x + y = 7 + 13
         = 20

Thus, the value of (x + y) is 20.

Hence, Option 1. is correct.


Hope it helps.

Answer 2

udufyghufjdjdidididiididjd