In the given figure, line AC intersects BD at point O. If ∠1:∠2 = 2:3, what is the measure of ∠4?

114^{\circ}

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118^{\circ}

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78^{\circ}

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108^{\circ}

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Solution

The correct option is D $108^{\circ}$
Given that, ∠1:∠2 = 2:3
Let ∠1 = 2k and ∠2 = 3k, where k is the constant of proportionality.
∠1 + ∠2 = 180° [Linear pair]
⇒ 2k + 3k = 180°
⇒ 5k = 180°
⇒ k = 36°
Thus, $∠ 2 = 3 k = 3 \times 36 ° = 108 °$
Also, ∠4 = ∠2 [Vertically opposite angles]
∴ ∠4 = 108°

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