I have this, what seems basic triangle problem, and not certain if the given information is sufficient to solve the problem of finding an angle.
We have one main isoceles and another one inside of it.
I have attached here a diagram, and we wish to find the angle in red:
The labels blue means : lengths PQ = QR
The label green means : lengths QS = QT
The given angle PQS = 24 (deg)
We wish to find angle in red , angle RST.
I am trying to figure this out only using geometric principle without trying to use a system of algebraic equations. I tried to create parallel lines to help, but it did not, I tried to make use of principle of exterior angle theorem, but still could not get it.
Hope someone here can help me on this.
Best Answer
Let $\widehat{QRP}= \widehat{RPQ}=x$, so $\widehat{RQP}=180-2x$, so $\widehat{RQS}=156-2x$, so the sum of the angles $\widehat{QST}$ and $ \widehat{QTS}$ is $24+2x$, so they are both $x+12$, so $\widehat{RTS}=168-x$, so $\widehat{RST}=12$.