Answer:
- y = 4
- c = f = g = 145°
- d = h = 35°
Step-by-step explanation:
You want the measures of the angles in the parallel line figure shown, along with the value of y.
Parallel lines
Where parallel lines are crossed by a transversal, all of the obtuse angles have the same measure:
c = f = g = 145°
The acute angles are supplementary to the obtuse angles in this geometry, so ...
d = h = 180° -145°
d = h = 35°
Variable
The value of y can be found by equating the expressions for y, or by using the angle measure of the acute angles marked with y-expressions.
35° = (2y +27)°
8 = 2y . . . . . . . . divide by °, subtract 27
4 = y . . . . . . . . divide by 2
The value of y is 4.
__
Additional comment
As a check, we find (5y +15)° = (5·4 +15)° = 35°, matching the other acute angles in the figure.
