Question

⑧ In the adjacent fig., AB ‖‖ CD & CD ‖‖ EF. If EA ⊥ AB & ∠BEF = 55°, then find the value of x, y & z . 3

Answer 1

CORRECT QUESTION -

In the adjacent fig. AB ‖ CD & CD ‖ EF. If EA ⊥ AB & ∠BEF = 55°, then find the value of x, y & z .

CORRECT SOLUTION -

Given :

AB ‖ CD ‖ EF. Also, EA ⊥ AB & ∠BEF = 55°.

Solⁿ :

CD ‖ EF & DE is the transversal.

⇒ y + 55° = 180° (Co. int. ∠s)

⇒ y = 180° - 55°

⇒ y = 125°

Again, AB ‖ CD & BD is the transversal.

⇒ x = y = 125° (Corresponding ∠s)

⇒ x = 125°

Also, AB ‖ EF & AE is the transversal. (AB ‖ CD ‖ EF)

⇒ ∠BAE + ∠FEA = 180° (Co. int. ∠s)

⇒ 90° + (z + 55°) = 180°

⇒ 90° + 55° + z = 180°

⇒ 145° + z = 180°

⇒ z = 180° - 145°

⇒ z = 35°

∴ The values of x, y & z are 125°, 125° & 35° respectively.