Answer:
The measure of [tex]\bold {\angle4}[/tex] is [tex]\bold{ 70^\rm{o}}[/tex].
Step-by-step explanation:
Given,
Lines a and b are parallel to each other and have transversal f.
The value of [tex]\bold{\angle 1}[/tex] is 110°.
To find: The value of [tex]\bold{\angle 4}[/tex].
As shown in the diagram [tex]\bold{\angle 1}[/tex] and [tex]\bold{\angle 2}[/tex] lies on line f.
Therefore, the sum of these angles will be [tex]\bold{180^\rm{o}}[/tex].
[tex]\begin{aligned}\angle1+\angle2&=180^\rm{o}\\\angle110+\angle2&=180^\rm{o}\\\angle 2&=70^\rm{o} \end{aligned}[/tex]
Now, [tex]\bold{\angle 2}[/tex] and [tex]\bold{\angle 4}[/tex] are vertical opposite angles.
Therefore, [tex]\bold {{\angle4}=70^\rm{o}}[/tex]
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