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In a pentagon...

Question

In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find ∠E.

120°

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110°

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130°

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100°

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Solution

The correct option is A 120°
Let the measure of the angles are 3x, 4x and 5x.
Thus,
$∠ A + ∠ B + ∠ C + ∠ D + ∠ E = 540 °$
$3 x + (∠ B + ∠ C) + 4 x + 5 x = 540 °$
$12 x + 180 ° = 540 °$
$12 x = 360 °$
$x = 30 °$
Thus, the measure of angle E will be $4 \times 30 ° = 120 °$ .

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