In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.

A. 20

B. 30

C. 120

D. 180

Answer: The measure of third angle is 120°

Step-by-step explanation:

Let the measurement of first angle is x degree,

Then according to the question,

The measurement of second angle = 2x degree

While, the measurement of third angle = 6x degree,

Since, the sum of all three angles of a triangle = 180°

⇒ x + 2x + 6x = 180°

⇒ 9x = 180°

⇒ x = 20°

Hence, the measurement of third angle = 6x = 6*20° = 120°

⇒ Option C is correct.

To solve this, I set angle one as x, since we don't know the value of it yet. Angle 2 is twice the first, I made it 2x, and made the third 3x by the same logic. We know that a triangles angles add up to 180 degrees. This means we can make the equation x+2x+3x=180. This simplifies to 6x=180 and so we get the answer that the first angle is 30 degrees.