Question

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'.

• A. ${150}^{\circ }$
• B. ${60}^{\circ }$
• C. ${20}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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 = ${30}^{\circ }$