Question

What is m∠PTS? Enter your answer in the box. °

Answer 1

Answer:

$m\angle PTS = 55\°$

Step-by-step explanation:

Given:

$m\angle PTS = [11(y-10)]\°$

$m\angle RTQ = (4y-5)\°$

We need to find the $m\angle PTS$

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."

$m\angle PTS =m\angle RTQ$

$11(y-10)=4y-5$

Applying distributive property we get;

$11y-110=4y-5$

Combining like terms we get;

$11y-4y=-5+110\\\\7y=105$

Dividing both side by 7 we get;

$\frac{7y}{7}=\frac{105}{7}\\\\y=15$

Substituting the value of 'y' we get;

$m\angle PTS = [11(y-10)]\°= [11(15-10)]\°= 55\°\\\\m\angle PTS = 55\°$

Hence The Final Answer is $m\angle PTS = 55\°$