- The figure given shows two parallel lines and a transversal line passing through them. This means that we would use the theorems of corresponding, alternate and/or vertically opposite angles to solve the question.
- Let us analyze these angles using the theorems mentioned above.
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The diagram thus looks like this:
- Next, we know that "Angles on a straight line are supplementary". That is they add up to 180°.
- Using this theorem, we have that:
[tex]\begin{gathered} \angle QST+\angle QSR=180\degree \\ But\text{ we know that }\angle QSR=45\degree^{} \\ \angle\text{QST}+45\degree=180\degree \\ \text{Subtract }45\degree\text{ from both sides} \\ \angle\text{QST}=180\degree-45\degree \\ \\ \therefore\angle QST=135\degree \end{gathered}[/tex]
Answer
