Triangle with the 116° angle in it is a isosceles triangle. So the bottom two angles are the same. (also says it in the question) To find them do:
180 - 116 = 64
64 ÷ 2 = 32
Bottom two angles are 32.
To double check: This should add up to 180° since triangles add up to 180°.
32 + 32 + 116 = 180
Angle ABD must be 58°
Because if angle CBD is 32. And is in a 90° angle. The angle on the other side will be 90 - 32 which is 58.
All triangles add up to 180° so to find the missing angle on the second triangle:
55 + 58 = 113
180 - 113 = 67
Angle ADB = 67°
So x = 116 + 67
Which is 183.
Because the angle around a point is 360°
360 - 183 = 177
x = 177
Double check: This should add up to 360°
116 + 183 + 67 = 360°
:)