1. Let x represent the missing angle.
The sum of angles in a triangle is 180°
65° + 57° +x =180
122° +x=180°
x=180-122
x=68°
2. Let y represent the missing angle.
Then
y+90°+40°=180°
y+130°=180°
y=180°-130°
y=50°
3. Let the missing angle be t, then
t+20°+130°=180°
t+150° =180°
t=180°-150°
t=30°
4. Let the missing angle be m, then
m+85°+50°=180°
m=180°-50°-85°
m=180-135°
m=45°
5. Let the missing angle be e, then by the exterior remote angle theorem:
137°=102° +e
137-102=e
e=35°
6. Let the unknown angle p, be the missing angle.
Then by vertical angle property and exterior angle property:
p=35° +100°
p=135°
7. Let g be the missing angle, then
g+20°+30°=180°
g+50°=180°
g=180°-50°
g=130°
8)
Let v be the missing angle:
By angle on straight line, and exterior angle theorem property,
g=(180-155)+60°
g=25°+60°
g=85°