Final answer:
In this diagram, (15x + 5)° and (14x + 11)°, are both alternate exterior angles, they are congruent and their measurement is 95°.
Step-by-step explanation:
The two angles given, (15x + 5)° and (14x + 11)°, are both alternate exterior angles that lie outside the parallel lines, with each lying in the opposite direction to each other on the transversal that crosses the parallel lines.
Alternate exterior angles are a pair of angles formed by a transversal line intersecting two parallel lines.
When a transversal crosses two parallel lines, the alternate exterior angles are located on opposite sides of the transversal and on the outside of the parallel lines.
These angles are congruent, meaning they have equal measures.
This type of angle pair is: alternate exterior angles.
The relationship that exist between this type of angle pair is: alternate exterior angles are congruent.
Therefore, (15x + 5)° = (14x + 11)°.
Since, they are equal so,
(15x + 5)° = (14x + 11)°
x = 6
Plug in the value of x into the expression of each missing angle to find their measures:
(15x + 5)° = 15(6) + 5 = 90 + 5 = 95°
(14x + 11)° = 14(6) + 11 = 84 + 11 = 95°
So, the missing angle measures is 95°.