From the figure given, find the sum of x, y and z in degrees.

190

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Solution

The correct option is A 190
$From the figure B E | | D C$
$∠ E B C + ∠ z = 180 ° (Co interior angles)$

$70^{\circ} + ∠ z = 180 ° ∠ z = (180 - 70) ° = 110 ° ∠ A B E = ∠ z = 110 ° (Corresponding angles)$
$∠ x = 150^{\circ} - ∠ A B E = 150^{\circ} - ∠ z = 150^{\circ} - 110^{\circ} = 40^{\circ}$

$Since A E ∥ B D, y = x as they are alternate angles. ∠ y = 40^{\circ}$

$The required sum = x + y + z = 40^{\circ} + 40^{\circ} + 110^{\circ} = 190^{\circ}$

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