If we have the following figure:
Angles A and B are consecutive interior angles, So the type is consecutive interior.
Angle B has the same value as Angle C because they are opposite by vertex and C and A are supplementary. It means that B and A are also supplementary angles. So, the relationship is supplementary.
If two angles are supplementary, the sum of them is 180, so we can write the following equation:
A + B = 180
(-3 + 14x) + (13x - 6) = 180
Solving for x, we get:
-3 + 14x + 13x - 6 = 180
27x - 9 = 180
27x = 180 + 9
27x = 189
x = 189/27
x = 7
Finally, The value of the missing angles are:
-3 + 14x = -3 + 14*7 = 95
13x - 6 = 13*7 - 6 = 85
Answers:
Type: consecutive interior
Relationship: Supplementary
Value of x: 7
Value of the missing angles: 85 and 95 degrees