Answer:
z = 13°
Step-by-step explanation:
Concept: Vertical Angle Theorem
Vertical angles are the pairs of opposing angles formed by the intersection of two lines. They are directly across from each other. The Vertical Angle Theorem states that if two lines cross at a single point, then vertical angles are congruent.
Now it's time to apply the theorem. As you can see from the diagram, (12z)° is directly across from 156°, making them vertical angles. Therefore, by the Vertical Angle Theorem, (12z)° ≅ 156° (≅ means congruent, which, for angles, means they're equivalent). From now on, it's just a little algebra. You divide both sides by 12 to get z by itself, getting [tex]\frac{12z}{z}[/tex] ≅ [tex]\frac{156}{12}[/tex] ⇒ z ≅ 13. You can replace ≅ with the equal sign and you get z = 13.
Therefore, z = 13°.
