Question

What is m∠PTS?

Enter your answer in the box.

°

Answer 1

`m\angle PTS = 55\°`

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;

`(7y)/(7)=(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\°`