Question

A ray is drawn from a point on a line. If one of the angles formed is five times the other one, then find both the angles.

• A. ${45}^{\circ }$ and ${225}^{\circ }$
• B. ${30}^{\circ }$ and ${150}^{\circ }$
• C. ${15}^{\circ }$ and ${75}^{\circ }$
• D. ${60}^{\circ }$ and ${300}^{\circ }$

Answer 1

The correct option is B

${30}^{\circ }$ and ${150}^{\circ }$

Let the smaller angle measure x degrees.
So, the measure of the larger angle will be 5x degrees.

If a ray is drawn from a point on a line then the sum of the measures of the angles on either side will be 180 degrees.

So,
x + 5x = 180 degrees

or, 6x = 180 degrees

or, x = 30 degrees

Thus, the measure of the smaller angle = x = 30 degrees
And the measure of the larger angle = 5x
$=5\times 30$
= 150 degrees