+0  
 
+1
38
1
avatar

The interior angle measures of a pentagon form an arithmetic progression. The difference between the largest and smallest angle measures is 48 degrees. Find the measure of the smallest angle, in degrees.

 Nov 12, 2020
 #1
avatar+112375 
+1

Call  the common difference between the angles,  D

 

And call the measure of the  smallest angle, A

 

And we  know  that the sum of the interior angles =  (5-2) (180)  = 3 *180  = 540°

 

So  we  have  that

 

A + (A + D )  + (A + 2D)  + (A + 3D) + (A + 4D)  = 540

 

5A + 10D  = 540    (1)

 

And we know that    (A + 4D)  - A  = 48

So, simplifying.......4D  = 48

D = 12    (2)

 

Sub  (2)  into (1)  and we have that

 

5A  + 10(12)  = 540

 

5A  + 120  = 540

 

5A  =  540 -120

 

5A  = 420

 

A = 420/5  =  84°

 

cool cool cool

 Nov 12, 2020

41 Online Users

avatar
avatar
avatar