To find the values of x and z, apply the opposite angles theorem.
Opposite angles are angles that can be said to be non-adjacent angles formed by two intersecting lines.
Opposite angles are congruent.
• Measure of angle Z:
∠z and 110 are opposite angles.
Thus, we have:
m∠z = 110°
• Value of x:
Given that total measure of angles = 360
We have:
[tex](5x-20)=\frac{360-110-110}{2}[/tex]
Let's solve for x:
[tex]\begin{gathered} 5x-20=\frac{140}{2} \\ \\ 5x-20=70 \\ \\ \text{Add 20 to both sides:} \\ 5x-20+20=70+20 \\ \\ 5x=90 \end{gathered}[/tex]
Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{90}{5} \\ \\ x=18 \end{gathered}[/tex]
ANSWER:
x = 18
z = 110°
