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The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is 126 degrees, what is the measure of the second largest angle, in degrees?

 Jun 1, 2021
 #1
avatar+2205 
+1

The smallest and largest angle will sum up to 180. 

That means that 180 - 126 = 54 is the small angle. 

54 __  __  126

Can you figure out the blanks?

 

=^._.^=

 Jun 1, 2021
 #2
avatar+121056 
+1

Let  the  smallest  angle  = a

Let  the  common difference = d

 

So

 

a  +  3d  =   126   ⇒   a   =  126 -  3d    ( 1)

 

And....the  sum of the angle measures  =  360

 

a  + (a + d)  +  (a + 2d)  + 126   =  360           (2)

 

Sub (1)  into (2)

 

126 - 3d  +  126 - 2d  + 126 - d  + 126  = 360

 

504  -  6d   =  360

 

504   - 360   =  6d

 

144  =  6d

 

d = 144 / 6     =    24

 

The second largest  angle  =   126  -  24    =   102°

 

cool cool cool

 Jun 1, 2021

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