What is the size of the other orange angle? Why?
- it's obviously equal to the visible angle x, which in the default position is 100 degrees. You'd want to encourage learners to recall the phrase: "vertically opposite angles are equal"
What is the size of the blue angle at the top? What about the blue angle at the bottom?
- theyre both equal to 180 - x so in the example I gave will mean they're 80 degrees each.
How did you figure this out? Is there another way to figure this out using a different rule?
- some learners add the orange angles, subtract from 360 and then halve the answer. Algebraically 0.5*(360 - 2x), by using vertically opposite angles twice and the angle sum at a point.
-others solve this by applying angles on a straight line twice: once to calculate the upper blue angle and once to find the lower blue angle.
This hints at a neat method to prove that vertically opposite angles are equal. You should try to lead learners to discover this proof- ideally in algebra:
1. find the upper blue angle is 180 - x by angles on a straight line
2. find the right hand orange angle is 180 - (180 - x) = x
