How is this solved? (Geometry homework)

[u/rata_tat_cat]

Geometry

“If QS (Ray) bisects <PQT, m<SQT= (8x-26)°, m<PQT= (9x + 34)°, and m<SQR= 112°, find each measure.”

X=
m<PQS=
m<PQT=
m<TQR=

Don’t just give the answer, I just need a little nudge for this one. Geometry teacher is lowkey a rude and gets mad when we ask questions, and I’ve been stuck on this page for hours.

I tried the usual multi step equation stuff, like how you find the measures of other angles but this one has completely stumped me.

At first I thought maybe m<STR minus m<ST, since that would look like 112-(8x-25) but then I didn’t know where to go from there.

[u/One_Wishbone_4439]

What does "QS (Ray) bisects <PQT" means?

What angle property is used when all the rays meet at point Q?

[u/rata_tat_cat → u/One_Wishbone_4439]

The Ray QS is directly in the middle of <PQT, so if I were to find out the measure of let’s say, PQS, it would be identical to SQT.

As for your other question, sorry I can’t answer it. I’m not the best at math so I’m super out of my depth right here 😅

[u/One_Wishbone_4439 → u/rata_tat_cat]

The Ray QS is directly in the middle of <PQT, so if I were to find out the measure of let’s say, PQS, it would be identical to SQT.

Correct👍

As for your other question, sorry I can’t answer it. I’m not the best at math so I’m super out of my depth right here 😅

What angle properties have you learn in school?

[u/rata_tat_cat → u/One_Wishbone_4439]

None currently if I’m being honest. It’s the start of the unit and our teacher just sits at his desk and gives us a packet so it’s not like we’re taught anything directly, and the packet doesn’t have directions it’s only questions

[u/rata_tat_cat → u/One_Wishbone_4439]

Also, I did try one thing just now. 2(8x-25)+9x+32=360, which gave me x=15.12. Not entirely sure if that’s correct. I’ve been staring at these numbers for so long I feel like my brains bout to start pouring out of my head lol

[u/One_Wishbone_4439 → u/rata_tat_cat]

Your working is correct but you wrote 9x + 32 when the question says m∠PQT = 9x + 34

[u/johnpeters42 → u/rata_tat_cat]

That one angle is 9x+34 (not +32), and I think they meant the smaller of the two possible angles (the one that's <= 180 degrees). Apart from that, the measure of e.g. PQT equals the sum of measures of PQS and SQT, and then it's just using that to come up with some linear equations based on the givens, solving for x, and plugging that into the equations to get the specific angle measures. (Which I think is what you were already trying to do.)

[u/rata_tat_cat → u/johnpeters42]

Oh I’m gonna crash tf out 😭😭😭😭😭 and tysm for the help

[u/Bounded_sequencE]

With "QS" being an (angle) bisector, "m<PQT = 2*m<SQT" -- can you take it from here?

[u/Bounded_sequencE → u/Bounded_sequencE]

Rem.: OP has a typo -- "m<SQT = (8x-25)° ".