+64 The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures $120^{\circ}$, what is the measure of the smallest angle?
Since a trapeziod is a quadrilateral, the sum of the angles is 360 degrees. Let x represent the difference between each term in the arithmetic sequence. This means that 120+(120-x)+(120-2x)+(120-3x)=360. Solving for x, you have that the common difference of each term in the arithmetic sequence is 20. The smallest angle is (120-3x), so substituting 20 for x, you get 120-3*20=60.
The measure of the smallest angle is 60 degrees.
Since a trapeziod is a quadrilateral, the sum of the angles is 360 degrees. Let x represent the difference between each term in the arithmetic sequence. This means that 120+(120-x)+(120-2x)+(120-3x)=360. Solving for x, you have that the common difference of each term in the arithmetic sequence is 20. The smallest angle is (120-3x), so substituting 20 for x, you get 120-3*20=60.
The measure of the smallest angle is 60 degrees.
+876 The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures 120 degrees, what is the measure of the smallest angle?
Let a be the smallest angle
Let n be the difference between two consecutive angles
a+(a+n)+(a+2n)+(a+3n)=360 (1)
a+3n=120 (2)
Substituting, we have: a+(a+n)+(a+2n)+120=360
a+a+n+a+2n=240
(a+a+a)+(n+2n)=240
3a+3n=240
a+n=80 (3)
(3) * 3 = 3a + 3n = 240 (4)
(4) - (2) => 2a = 120
a = 60 degrees
60 degrees
