Answer:
[tex]m\angle PTS = 55\°[/tex]
Step-by-step explanation:
Given:
[tex]m\angle PTS = [11(y-10)]\°[/tex]
[tex]m\angle RTQ = (4y-5)\°[/tex]
We need to find the [tex]m\angle PTS[/tex]
Solution:
Now we know that:
By Vertical angles theorem which states that;
"Angles that are opposite each other and formed by two intersecting straight lines, are congruent."
[tex]m\angle PTS =m\angle RTQ[/tex]
[tex]11(y-10)=4y-5[/tex]
Applying distributive property we get;
[tex]11y-110=4y-5[/tex]
Combining like terms we get;
[tex]11y-4y=-5+110\\\\7y=105[/tex]
Dividing both side by 7 we get;
[tex]\frac{7y}{7}=\frac{105}{7}\\\\y=15[/tex]
Substituting the value of 'y' we get;
[tex]m\angle PTS = [11(y-10)]\°= [11(15-10)]\°= 55\°\\\\m\angle PTS = 55\°[/tex]
Hence The Final Answer is [tex]m\angle PTS = 55\°[/tex]
