Grade 6 Lines and Angles Ex 2.2

Question 1: Can you find the angles in the given pictures? Draw the rays forming any one of the angles and name the vertex of the angle.

Answer:
Angles can be found in all four items where two straight parts meet at a corner or point.

Question 2: Draw and label an angle with arms ST and SR.

Answer:
The common letter in both arms is S, which means S is the vertex. The two rays shoot outwards toward points T and R.

Vertex: \(S\)
Arms: Ray \(ST\) and Ray \(SR\)
Angle Name: \(\angle TSR\) or \(\angle RST\)

Question 3: Explain why \(\angle APC\) cannot be labelled as \(\angle P\).

Answer:
Labeling the angle as \(\angle P\) is incorrect because multiple lines split from point \(P\), creating more than one angle at that single vertex.

As shown above, \(\angle P\) could mean \(\angle APB\), \(\angle BPC\), or the entire \(\angle APC\). Three letters must be used to remove this ambiguity.

Question 4: Name the angles marked in the given figure.

Answer:
There are three visible angles formed by the intersecting rays in the diagram:

Top interior angle: \(\angle APB\)
Bottom interior angle: \(\angle BPC\)
Entire main angle: \(\angle APC\)

Question 5: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C? Write them down, and mark each of them with a curve.

Number of Lines: Exactly 3 lines can be drawn.
Names of the Lines: Line \(AB\), Line \(BC\), and Line \(CA\).
Number of Angles: Exactly 3 angles are formed inside the figure.
Names of the Angles:
- \(\angle ABC\) (or \(\angle B\) at vertex \(B\))
- \(\angle BCA\) (or \(\angle C\) at vertex \(C\))
- \(\angle CAB\) (or \(\angle A\) at vertex \(A\))

Question 6: Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C, D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C, D? Write them down, and mark each of them with a curve.

Number of Lines: Exactly 6 lines can be drawn.
Names of the Lines: Line \(AB\), Line \(BC\), Line \(CD\), Line \(DA\), Line \(AC\), and Line \(BD\).
Number of Angles: A total of 12 single angles can be named from the structure created by the intersecting diagonals:
- At Vertex A: \(\angle DAB\), \(\angle DAC\), \(\angle CAB\)
- At Vertex B: \(\angle ABC\), \(\angle ABD\), \(\angle DBC\)
- At Vertex C: \(\angle BCD\), \(\angle BCA\), \(\angle ACD\)
- At Vertex D: \(\angle CDA\), \(\angle CDB\), \(\angle BDA\)