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In the adjoining figure of rectangle ABCD and $∠ ABE = 30 °$ , $∠ CFE = 144 °$ .Find the measure of $∠$ BEF

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64 °

34 °

84 °

44 °

answer is C.

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Detailed Solution

Given is a figure,

∠ CFE = 144 °

∠ ABE = 30 °

The angles of rectangles are

90 °

each.

∠ ABC = 90 °

, so,

∠ FBE = 90 ° - 30 °

And

∠ EFB = 180 ° - 144 °

(Linear Pair)
In triangle BEF, the sum of angles of a triangle is 180

°

∠

BEF +

∠

EFB+

∠

FBE

= 180 °

\Rightarrow

∠

BEF+(

180 ° - 144 °) + (90 ° - 30 °) = 180 °

\Rightarrow

∠

BEF+36

°

60 ° = 180 °

\Rightarrow

∠

BEF+96

° = 180 °

\Rightarrow

∠

BEF

= 180 ° - 96 °

\Rightarrow

∠

BEF

= 84 °

Thus, the value of

∠

BEF in the given rectangle ABCD is

84 °

.
Therefore, option (3) is correct.

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