In the figure, angle ABE = angle ECD and angle EBD = angle ACE. If angle BAC = 80 degrees and angle BEC = 100 degrees, then find obtuse angle BDC.
+128408 Let angles ABE and ECD = x
And let angles EBD and ACE = y
So in quadrilateral ABCE angle BCE = 360 - 100 = 260°
And in a quadrilateral, the sum of the interior angles = 360°
So we have that
80 + 260 + x + y = 360
340 + x + y = 360
x + y = 20
And in quadrilateral BECD we have that
100 + x + y + (360 - angle BDC ) = 360
100 + 20 + 360 - angle BDC = 360
120 - angle BDC = 0
Angle BDC =120°
