Given a quadrilateral with angles measuring 102 degrees, 80 degrees, and 98 degrees, what is the measure of the remaining angle?

Given a quadrilateral with angles measuring 102 degrees, 80 degrees, and 98 degrees, what is the measure of the remaining angle?

• A. 70 degrees
• B. 80 degrees
• C. 90 degrees
• D. 100 degrees

Answer: (B)

To find the measure of the remaining angle in a quadrilateral, you can use the fact that the sum of the interior angles of a quadrilateral is always 360 degrees. In this case, you have three angles already given: 102 degrees, 80 degrees, and 98 degrees. First, add these angles together: 102 + 80 + 98 = 280 degrees. Now, subtract this sum from 360 degrees to find the measure of the fourth angle: 360 - 280 = 80 degrees. Thus, the measure of the remaining angle is indeed 80 degrees. This value matches one of the choices provided and confirms the calculations based on the properties of quadrilaterals. Understanding this principle allows you to solve similar problems related to polygon angle sums.

To find the measure of the remaining angle in a quadrilateral, you can use the fact that the sum of the interior angles of a quadrilateral is always 360 degrees.

In this case, you have three angles already given: 102 degrees, 80 degrees, and 98 degrees. First, add these angles together:

102 + 80 + 98 = 280 degrees.

Now, subtract this sum from 360 degrees to find the measure of the fourth angle:

360 - 280 = 80 degrees.

Thus, the measure of the remaining angle is indeed 80 degrees. This value matches one of the choices provided and confirms the calculations based on the properties of quadrilaterals. Understanding this principle allows you to solve similar problems related to polygon angle sums.