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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?

 May 1, 2021

Best Answer 

 #1
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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.

 May 1, 2021
 #1
avatar
+2
Best Answer

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.

Guest May 1, 2021
 #2
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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


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