Question

In figure, if AB II CD, CD II EF and 𝑦∶𝑧=3∶7, then find 𝑥

Answer 1

Given, AB ∥ CD, CD ∥ EF and y：z = 3：7.
Since, AB ∥ CD and CD ∥ EF then AB ∥ EF.
Hence x = z (Alternate exterior angles are equal).
And x + y = 180° (Sum of co-interior angles is 180°).
We can write, y + z = 180°
Let, y = 3a and z = 7a

(y ：z = 3 ：7, given).

So, y + z = 180°

3a + 7a = 180°

10a = 180°

a = 18.

Since x = z = 7a

Then x = 7×18 = 126°