A quadrilateral has interior angles measuring 120 degrees, 70 degrees, and 100 degrees. What is the measure of the fourth angle?

A quadrilateral has interior angles measuring 120 degrees, 70 degrees, and 100 degrees. What is the measure of the fourth angle?

• A. 70 degrees
• B. 40 degrees
• C. 60 degrees
• D. 100 degrees

Answer: (A)

In any quadrilateral, the interior angles add up to 360 degrees. Add the three given angles: 120 + 70 + 100 = 290. The fourth angle must bring the total to 360, so 360 − 290 = 70 degrees. So the fourth angle measures 70 degrees. If a different value were used, the total of all four angles wouldn’t reach 360 degrees (for example, 40 would give 330, 60 would give 350, and 100 would give 390).

In any quadrilateral, the interior angles add up to 360 degrees. Add the three given angles: 120 + 70 + 100 = 290. The fourth angle must bring the total to 360, so 360 − 290 = 70 degrees.

So the fourth angle measures 70 degrees. If a different value were used, the total of all four angles wouldn’t reach 360 degrees (for example, 40 would give 330, 60 would give 350, and 100 would give 390).