The figure shows a pair of parallel lines with a transversal drawn through them. This is a two-part question. The first part says, what name is given to the pairs of coloured angles highlighted in the figure? Interior angles, exterior angles, corresponding angles, or straight angles.
So in the diagram, the parallel lines are the pair of horizontal lines and the transversal is the line highlighted in pink, which cuts through each of them. We’re asked to look at the pairs of coloured angles. Let’s look first of all at the positions of the pair of angles highlighted in green. Each of these angles are on the same side of the transversal. They’re on the right. They’re also the same side of the parallel lines. They are above them.
These two criteria are what is necessary in order for a pair of angles to be corresponding angles. The same is true if we look at the pair of red angles. They’re on the same side of the transversal — the right. And they’re on the same side of the parallel lines — below. Therefore, these are also an example of corresponding angles.
The exact same is true regarding the pair of blue angles and the pair of orange angles. And therefore, our answer to the first part of the question is that the name given to the pairs of coloured angles is corresponding angles.
The second part of the question asks, what do you notice regarding the measures of two corresponding angles? This is why I didn’t write this part down straightaway because it rather gives the game away for the first part. The options are they are supplementary, they are complementary, or they are equal.
Let’s just remind ourselves first of all what is meant by the term supplementary and complementary. A pair of angles are supplementary if their sum is 180 degrees, a pair of angles are complementary if they sum to 90 degrees, and of course, a pair of angles are equal if their measures are the same.
So looking at the diagram, we can see that the measures of corresponding angles are the same in each case. Both orange angles are 135 degrees as are the two red angles and the blue angles are 45 degrees as are the two green angles. Therefore, our answer to the second part of the question regarding the measures of corresponding angles is that they are equal.