Question

1. In the given fig. I is parallel to m and p ll q. Find the measure of each of the angles a,b,c,d. [4]
P
q
b
a
100°
с
d​

Answer 1

$\sf\blue{SolutioN:-}$

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∠D = 100° [ Vertically opposite angle]

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∠1 + 100° = 180° [ Linear pair ]

∠1 = 180° - 100°

∠1 = 80°

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If P is parallel to Q and L parallel to M

So, It forms parallelogram.

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We know that, Opposite angle of parallelogram are equal.

So, ∠1 = ∠a = 80°

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∠a + ∠b = 180° [ Co - interior angles]

80° + ∠b = 180°

∠b = 180° - 80°

∠b = 100°

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∠b = ∠c = 100° [ Opposite angles of parallelogram are equal.

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Hence,

∠a = 80°

∠b = 100°

∠c = 100°

∠d = 100°

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