Answer:
[tex]m\angle 3=136^{\circ}[/tex]
Step-by-step explanation:
We are given that
Measure of intercepted arc are
[tex]46^{\circ},42^{\circ}[/tex]
We have to find the measure of angle 3.
We know that
Internal angle=half the sum of measures of its intercepted arc.
Using this property
Measure of angle 4=[tex]\frac{1}{2}(46+42)=44^{\circ}[/tex]
Measure of angle 4 +measure pf angle 3=180 degrees (linear pair)
Substitute the values then we get
[tex]44^{\circ}+m\angle 3=180^{\circ}[/tex]
[tex]m\angle 3=180-44=136^{\circ}[/tex]
Hence, the [tex]m\angle 3=136^{\circ}[/tex]
