Question

5.
In figure
figure if
if AB||CD, angle BAE is 132 and
angle AEC is 148 then find the value of angle
DCF.​

Answer 1

Given:

AB // CD

∠BAE = 132°

∠AEC = 148°

To find:

The value of ∠DCF

Construction:

Draw a line EF from vertex E such that EF // AB // CD

Solution:

We can say that,

∠AEC = ∠AEF + ∠FEC = 148° ...... (i)

Also, ∵ EF //AB (from construction)

∴ ∠BAE + ∠AEF = 180° ...... [sum of interior angles is 180°]

⇒ 132° + ∠AEF = 180°

⇒ ∠AEF = 180° - 132°

⇒ ∠AEF = 48° ...... (ii)

On substituting (ii) in (i), we get

∠AEF + ∠FEC = 148°

⇒ 48° + ∠FEC = 148°

⇒ ∠FEC = 148° - 48°

⇒ ∠FEC = 100° ...... (iii)

Now, ∵ EF // CD (from construction)

∠FEC = ∠DCF ....... [corresponding angles]

from (iii), we get

∴ ∠DCF = 100°

Thus, $\boxed{\bold{The\:value\:of\:\angle DCF = \underline{100\°}}}$.

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