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The angles ∠PTQ and ∠QTS are supplementary, so they add to 180°. Hence, option B is the correct option.
How are angles on a straight line related?
Angles on a straight line will always add up to 180°, that is, they are supplementary angles.
How do we solve the given question?
In the figure, we are given a straight line PS. We are asked to determine the relation between ∠PTQ and ∠QTS.
As we can see ∠QTS is made up of two angels, ∠QTR and ∠RTS.
The three angles, ∠PTQ, ∠QTR, and ∠RTS constitute the straight line PS.
∴ ∠PTQ + ∠QTR + ∠RTS = 180° (As angles on a straight line are supplementary, that is, they add to 180°)
Replacing ∠QTS = ∠QTR + ∠RTS in the above equation, we get
∠PTQ + ∠QTS = 180°.
∴ The angles ∠PTQ and ∠QTS are supplementary, so they add to 180°. Hence, option B is the correct option.
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