Angles question (1 Viewer)
- Thread starter smithjohn
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Is there any similarity involved in this question?
The only angle I'm struggling to prove is ∠TSR.
The only angle I'm struggling to prove is ∠TSR.
No all they give us is that info. I got all angles, worked out angle PSR = 110 and angle PTQ = 125 but how can you find the angle PST. I have no clue all the answer says is 35 degrees
I'm thinking finding ∠TSR or ∠STQ is most likely what we need to do next. I don't see what else can be done.
I found angle PSR = 110 and PTQ = 125 using exterior angle of a triangle but still doesnt help
Oh lol, there are 2 isosceles triangles.
Not sure how much that helps, if at all.
Not sure how much that helps, if at all.
How would that help I see triangle TRQ and triangle PQR (isosceles triangle)
RSQ is also isosceles I believe.
If we can find the value of any one of these: <PTS, <TSR, <STQ, that should do it.
If we can find the value of any one of these: <PTS, <TSR, <STQ, that should do it.
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I think I found it:
- ΔTRQ is isosceles (∠QTR = ∠RQT = 55°)
Therefore QR = TR
- ΔSRQ is isosceles (∠QSR = ∠SQR = 70°)
Therefore QR = SR
But QR = TR
Therefore TR = SR, meaning ΔSRT is isosceles
- ∠TRS = 30°
Therefore ∠RTS = ∠RST = 75°
Now that we have the value of ∠RST, we can show that ∠PST is 35°
∠QSR = 70°
∠RTS = 75°
- PQ is a straight line:
Therefore: 180 - (70+75) = 35
Therefore ∠PST is 35°
- ΔTRQ is isosceles (∠QTR = ∠RQT = 55°)
Therefore QR = TR
- ΔSRQ is isosceles (∠QSR = ∠SQR = 70°)
Therefore QR = SR
But QR = TR
Therefore TR = SR, meaning ΔSRT is isosceles
- ∠TRS = 30°
Therefore ∠RTS = ∠RST = 75°
Now that we have the value of ∠RST, we can show that ∠PST is 35°
∠QSR = 70°
∠RTS = 75°
- PQ is a straight line:
Therefore: 180 - (70+75) = 35
Therefore ∠PST is 35°
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No worries!