Answer:
1. 31.67 degrees
2. 38 degrees
3.
PNQ = 117 degrees
LKQ = 102 degrees
4. XYV = 120 degrees
Step-by-step explanation:
1. Using sum of angles of a triangle = 180
angle ACB = 180 - 55.14 - 93.19 = 31.67
2.
FDE = 180-GDE = 180 - 135.11 = 44.89 [angles on a line are supplementary]
FED = HEJ = 97.11 [vertical angles]
DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees
3.
MLN = 180 - 82 = 98 [angles on a line are supplementary]
PNQ = 360 - 67 - 78 - 98 = 117 [sum of exterior angles of a polygon = 360]
LKQ = 180 - 78 = 102 [angles on a line are supplementary]
4.
WXY+YXZ = 180 [angles on a line are supplementary]
=>
3x + x = 180
=>
x = 180/4 = 45
Now solve for XYV
XYV = 360 - 135 - 60 - 45 = 120 [sum of interior angles of quadrilateral = 360]
Note: In the future, please limit the number of problems per question to three.
