Answer:
y° = 110°
z° = 26°
Step-by-step explanation:
Looking at the above geometry, we have two parallel lines , m and m
We have been asked to solve for y° and z°
Step 1
We solve for y°
On line n , we have can see that 70° and y° are CONSECUTIVE INTERIOR ANGLES
It is important to note that THE SUM OF TWO CONSECUTIVE INTERIOR ANGLES = 180°
Hence,
70° + y° = 180°
y° = 180° - 70°
y° = 110°
Step 2
Solve for z°
Looking at the geometric diagram we can see that
y° and (6z - 46) ° are ALTERNATE INTERIOR ANGLES
This means
y° = (6z - 46) °
In step 1 , we have already solved for y°
y° = 110°
Hence,
110° = (6z - 46) °
110° = 6z° - 46°
collect like terms
110° + 46° = 6z°
156° = 6z°
Divide both sides by 6
156°/6 = z°
z° = 26°
Therefore, the value y = 110° and the value of z = 26°
