Answer: 78
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Step-by-step explanation:
Focus on triangle BDH
The three inside angles of any triangle always add to 180 degrees.
B+D+H = 180
47+31+H = 180
78+H = 180
H = 180-78
H = 102
Angle BHD is 102 degrees.
It adds to angle x, aka angle BHC, to get 180 degrees. These two adjacent angles combine to a straight line.
(angle BHD) + (angle BHC) = 180
102 + x = 180
x = 180-102
x = 78
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Shortcut:
Focus on triangle BDH.
Use the remote interior angle theorem to add the given interior angles.
B+D = 47+31 = 78
This is equal to the exterior angle that is not adjacent to either interior angle mentioned. This refers to angle BHC, aka angle x.