Question

In the given figure, DE | | BC and MF | | AB. Find : (a) / ADE + / MEN (b) / BDE (c) / BLE

Answer 1

refer to the attachment

Answer 2

Given :-

• DE | | BC
• MF | | AB.
• ∠DBL = 40°
• ∠ECL = 50°

To Find :-

• ∠ADE + ∠MEN
• ∠BDE
• ∠BLE

Solution :-

Given that, DE || BC and BD is a transversal.

Therefore,

→ ∠ADE = ∠DBC {Corresponding angles.}

→ ∠ADE = 40°

Now,

MF II AB and DE is a transversal.

Therefore

→ ∠DEL = ∠ADE {Alternate angles.]

→ ∠DEL = 40°

Also,

→ ∠MEM = ∠DEL {Vertically opposite angles.}

→ ∠MEN = 40°

Hence,

→ ∠ADE + ∠MEN = 40° + 40° = 80°. (Ans.)

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Now,

DE || BC and BD is a transversal.

Therefore,

→ ∠DBC + ∠BDE = 180° {Co-interior angles on the same side of a transversal are supplementary.}

→ 40° + ∠BDE = 180°

→ ∠BDE = 180° - 40°

→ ∠BDE = 140° .(Ans.)

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Again ,

MF ll AB and BL is a transversal.

Therefore,

→ ∠DBL + ∠BLE = 180° {Co-interior angles on the same side of a transversal are supplementary.}

→ ∠40° + ∠BLE = 180°

→ ∠BLE = 180° - 40°

→ ∠BLE = 140° (Ans.)

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