Answer:
Third option is the right choice.
Step by step explanation:
We have been given an diagram and we are asked to choose the true statement about the diagram.
Let us see our all choices one by one.
1. [tex]m\angle5+m\angle6=m\angle1[/tex]
We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].
Therefore, 1st option is incorrect.
2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]
We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees. Therefore, 2nd option is also incorrect.
3. [tex]m\angle1+m\angle2=180^{o}[/tex]
We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.
4. [tex]m\angle2+m\angle3=m\angle5[/tex]
We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].
Therefore, our 4th option is also incorrect.
