Question

the sum of the measures of the angles of the quadrilateral in radian equals

Answer 1

Answer:

The Quadrilateral Sum Conjecture tells us the sum of the angles in any convex quadrilateral is 360 degrees. Remember that a polygon is convex if each of its interior angles is less that 180 degree.

Answer 2

Given:

A quadrilateral.

To find:

Sum of measures of the angles in radians.

Solution:

A quadrilateral is a polygon having four sides with four angles. On adding all the angles, the sum will be $360$°. But this is in degrees. The problem is asking for the sum in radians. To convert degrees into radians, multiply the number with $\frac{\pi }{180}$.

Here, the sum is measured in degrees. We will multiply $360$° with $\frac{\pi }{180}$ to determine the sum of measures of angles in radians.

Angle sum in radians = $360*\frac{\pi }{180}=2\pi$

Hence, the sum of measures of angles of a quadrilateral in radians is $2\pi$.

The sum of measures of angles of a quadrilateral in radians is $2\pi$.