SOLUTION: In the accompanying diagram of parallelogram ABCD, m∠B = 5x - 6, and m∠C = 3x + 10. Find the number of degrees in ∠D.

Algebra ->  Parallelograms -> SOLUTION: In the accompanying diagram of parallelogram ABCD, m∠B = 5x - 6, and m∠C = 3x + 10. Find the number of degrees in ∠D.       Log On


   

Question 1176613: In the accompanying diagram of parallelogram ABCD, m∠B = 5x - 6, and m∠C = 3x + 10.
Find the number of degrees in ∠D.

Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
parallelogram
so
AB=CD
AD=BC
m∠B = m∠D
m∠C =m∠A
given
m∠B+=+5x+-+6, and m∠C+=+3x+%2B+10
since the sum of all angles is 360, m∠B +m∠C=180

+5x+-+6%2B3x+%2B+10=180
+8x+%2B+4=180
+8x=180-4
+8x=176
+x=176%2F8
+x=22

find m∠B+=+5x+-+6
m∠B+=+5%2A22+-+6
m∠B+=+104 degrees
since m∠B = m∠D means m∠highlight%28D=104%29 degrees=> answer
check the other angles
m∠C+=+3x+%2B+10
m∠C+=+3%2A22+%2B+10
m∠C+=+76 degrees
then
m∠A+=+76 degrees

the sum of all angles is 104%2B104%2B76%2B76=360 degrees

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi



 2m∠B +  2m∠C  = 360°
(5x - 6) + (3x + 10) = 180°
       8x = 176
        x = 22 
  m∠D = m∠B = 5x-6 = 104°

76° + 104° + 76° + 104° = 360° checks
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