Ok guys ik that this isn't a part of academic but i wanna say a story ... since i had 15 subs ive always wanted 100 .. like so bad i been grinding making content and now im at 90 subs 999 Trendy is my YT .. bro that was my goal just 10 more wholesome subscriber and then *poof* you have made my day .. my next goal is .. if u sub ill give u brainliest .. my Yt is 999 Trendy.

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.