Answer:
∠3 = 52°
Step-by-step explanation:
Lets break down this problem. We are given two parallel lines (Line M and Line P). In between those lines we have a transversal or Line S. We are told to find ∠3.
- We know that ∠R, 62°, and ∠3 have to be supplementary to one another.
- In order to find ∠3 we need to work from the bottom up.
I will do my best to explain this
Ok, we need to find ∠T first by taking
[tex]180-144 = 36[/tex]
Note that ∠T = 66 °. We can use the Vertical angles theorem and find the angle opposite of ∠2. All the interior angles of a triangle must add up to 180°.
To find ∠2 of the triangle we take the following:
[tex]66+62 = 128\\180-128 = 52[/tex]
Therefore, ∠2 = 52°
Because of the alternate angles theorem, technically∠3 should equal 52° and ∠R should = 66°.
Lets check our work:
- The combination of ∠R + 62° + ∠3 = 180 as they are supplementary to one another
[tex]62+66+52 =180[/tex]
With all that said, ∠3 = 52°
I am happy to help with any other problems you might have in the future and I will continue to work hard in trying to provide the best answers :D
