Answer:
- x = 5
- a = f = 14°
- b = c = d = e = 166°
Explanation:
Given alternate interior angles at parallel lines have measures x +9 and 4x -6, you want to know the value of x and the measures of all of the angles.
Alternate interior angles
Where a transversal crosses parallel lines, alternate interior angles are congruent:
4x -6 = x +9
3x = 15 . . . . . . . . add 6-x
x = 5
The value of x is 5.
Other angles
In the figure shown, all of the acute angles are congruent, and all of the obtuse angles are congruent.
a = x +9 = 5 +9
a = 14 . . . . . degrees
f = a = 14°
The obtuse angles are supplementary to the acute angles:
b = c = d = e = 180° -a = 166°