182k views
5 votes
I need an answer and explanation please? Very much appreciated! <3​

I need an answer and explanation please? Very much appreciated! <3​-example-1
User Albzi
by
5.3k points

1 Answer

2 votes

Answer:

Explanation:

You need to know angles like PQT and the one labeled 148 equal 180, since putting them together makes a straight line and the relationship between "alternate exterior" and "alternate interior" angles. Basically they are the same

If you need a more in depth explanation on those angles let me know.

ANyway, we'll start with what I mentions at first;

PQT = 180 - 148 = 32

Then PQT and SRT are alternate interior angles so they are equal

RST = 180 - 104 = 76

then RST and TPQ are also alternate interior angles so both equal 76

Now, the sum of angles in a triangle are 180 so TPQ + PQT + QTP = 180 and RST + SRT + RTS = 180. Plugging in what we know gets us RTS = 180 - 108 = 72 = QTP.

You might be wondering how this helps, well, RTQ is a straight line, so PTR + QTP = 180. So that means PTR = 180 - QTP = 180 - 72 = 108

Let me know if something here doesn't make sense.

User Cristian Babarusi
by
5.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.