Question

When all the angles of a quadrilateral are written in descending order of their measures, each angle is 20° smaller than the previous angle. Write the measure of the smallest angle of the quadrilateral.

Answer 1

60°

Explanation:

that is the solution above

Answer 2

smallest angle = 60°

Explanation:

a quadrilateral has 4 interior angles

let n be the largest angle , then the next 3 angles in descending order are

n - 20

n - 20 - 20 = n - 40

n - 40 - 20 = n - 60 ← smallest angle

the sum of the interior angles in a quadrilateral is 360°

sum the 4 angles and equate to 360 to find value of n

n + n - 20 + n - 40 + n - 60 = 360

4n - 120 = 360 ( add 120 to both sides )

4n = 480 ( divide both sides by 4 )

n = 120

Then

smallest angle = n - 60 = 120 - 60 = 60°