In the following figure, if AB ∥ CD and EH is a transversal, what will be the measure of $∠ A F G$ ?

126^{\circ}

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136^{\circ}

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26^{\circ}

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36^{\circ}

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Solution

The correct option is A $126^{\circ}$
$∠ D G H = 54 °$ [Given]
$∠ C G H + ∠ D G H = 180 °$ [Linear pair of angles]
∴ $∠ C G H + 54 ° = 180 °$
$∠ C G H = 180 ° - 54 °$
$∠ C G H = 126 °$

$∠ A F G = ∠ C G H$ [Corresponding angles]
∴ $∠ A F G = 126 °$

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Question 30

In the given figure, lines PQ and ST intersect at O. If $∠ P O R = 90^{\circ}$ and
x:y = 3:2, then z is equal to

(a) $126^{\circ}$
(b) $144^{\circ}$
(c) $136^{\circ}$
(d) $154^{\circ}$

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In the following figure, if AB ∥ CD and EH is a transversal, what will be the measure of ∠AFG?

The correct option is A 126∘∠DGH=54° [Given] ∠CGH+∠DGH=180° [Linear pair of angles] ∴ ∠CGH+54°=180° ∠CGH=180°−54° ∠CGH=126° ∠AFG=∠CGH [Corresponding angles] ∴ ∠AFG=126°

In the following figure, if AB ∥ CD and EH is a transversal, what will be the measure of $∠ A F G$ ?

The correct option is A $126^{\circ}$
$∠ D G H = 54 °$ [Given]
$∠ C G H + ∠ D G H = 180 °$ [Linear pair of angles]
∴ $∠ C G H + 54 ° = 180 °$
$∠ C G H = 180 ° - 54 °$
$∠ C G H = 126 °$

$∠ A F G = ∠ C G H$ [Corresponding angles]
∴ $∠ A F G = 126 °$