In the figure, demonstrate that the angles with equal numbers are equal.
Answer the following with suitable theorems:
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Angles
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Theorems
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| \(\angle RQP\) \(=\) \(90^{\circ}\) | |
| \(\angle QRP\) \(+\) \(\angle RPQ\) \(=\) \(90^{\circ}\) | |
| \(\angle QRP\) \(=\) \(\angle PSQ\) | |
| \(\angle QPA\) \(+\) \(\angle QPB\) \(=\) \(180^{\circ}\) | |
| \(\angle PSQ\) \(+\) \(\angle PTQ\) \(=\) \(180^{\circ}\) |
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Answer variants:
Sum of the two acute angles in a right-angled triangle is \(90^{\circ}\)
The linear pair of angles are always supplementary
Angle in a semicircle is \(90^{\circ}\)
Angles in the same segment are equal.
Sum of opposite angles of a cyclic quadrilateral is \(180^{\circ}\).