1. The diagram includes 3 pairs of parallel lines. Find values for all angles on the page in terms of [math]\alpha[/math] and [math]\beta[/math], and add labels to the diagram. As you are doing so, make sure you think about the angle relationships you are using. Include angle relationship labels on angles within one step of the given angles, where space permits. Use angles on a line and angles on parallel line relationships only.[br][br]2. The diagram includes 3 pairs of parallel lines. Using only corresponding (c) (or alternate exterior/interior or co-interior/exterior angles), vertically opposite angles (v) and angles on a line (l) relationships, find and label all the angles, with both the value, and labels of the relationships used. Note that some angles will require use of angle rules multiple times, so the label may be cc, cv, cl etc. Some angles are found using both source angles, and a string should be included for each source, then followed by any further relationships used. e.g. [math]^{cc}_ccl[/math][br][br]3. The diagram includes 3 pairs of parallel lines. Find values for as many angles as you can using only one step angles on parallel lines and at a point relationships. Label each such angle with the value and the relationship used.[br][br]To make it simpler you may like to define additional angle labels as below:[br][math]\alpha^{\ast}=180^\circ-\alpha[/math][br][math]\beta^{\ast}=180^\circ-\beta[/math][br][math]\gamma=f\left(\alpha,\beta\right)[/math] for some linear function [math]f[/math] with [math]\gamma^{\ast}[/math] defined similarly to [math]\alpha^{\ast}[/math] and [math]\beta^{\ast}[/math].[br][br]Also, do you notice anything interesting about the values you record within the triangles? [br]Or the quadrilaterals?

Geogebra only enables labelling one angle on each pair of lines, or 2 on a three way intersection. (It is possible but not simple to use dots on every line to uniquely define angles of interest and label all angles.) This is intended to be a printed off task, so the above serves as a solution guide rather than a full solutions. The remaining values may be trivially retrieved by the teacher using angle at a point results.[br]For this solution [math]\gamma=\beta-\alpha[/math] although other useful definitions are possible