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In the diagram below, determine the value of x:

Guest Aug 2, 2017
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In the top triangle, the angle supplemental to 130°  = 50°

So.....the other angle in the top triangle is    = 85°

 

And in the quadrilatral, the angle supplemental to this =  95°

 

And in the leftmost triangle, again, the angle supplemental to 130° is 50°

So the missing angle in the triangle   is   180 - 50 - 30  = 100°

 

And the angle supplemental to this in the quadrilateral  = 80°

 

So.....the sum of the interior angles in the quadrilateral =  360

 

So we have that

 

360  = 95 + 80 + 130 + x      simplify

 

360  = 305 + x       subtract  305 from both sides

 

55°   = x

 

 

 

cool cool cool

CPhill  Aug 2, 2017

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