Two lines, line 1 and line 2 intersect at a point O and a ray, OX is drawn from the point of intersection. The ray divides the angle between the lines as shown. One of the angles is given, find the value of 'x'.

150^{\circ}

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60^{\circ}

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20^{\circ}

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30^{\circ}

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Solution

The correct option is D $30^{\circ}$
Given a ray is drawn from the point of intersection.
From the diagram, $30^{\circ}$ , 2x and 3x all lie on one the same side of the 'line 2',

So, sum of all three angles is $180^{\circ}$

$⟹ 30^{\circ}$ + 2x + 3x = $180^{\circ}$

$⟹$ 5x = $150^{\circ}$

$⟹$ x = $30^{\circ}$

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Two lines, line 1 and line 2 intersect at a point O and a ray, OX is drawn from the point of intersection. The ray divides the angle between the lines as shown. One of the angles is given, find the value of 'x'.

The correct option is D 30∘Given a ray is drawn from the point of intersection. From the diagram, 30∘, 2x and 3x all lie on one the same side of the 'line 2', So, sum of all three angles is 180∘ ⟹30∘ + 2x + 3x = 180∘ ⟹5x = 150∘ ⟹ x = 30∘