The diagram shows the parallelogram
𝐴𝐵𝐶𝐷. The diagram is drawn
accurately. Measure the length of 𝐴𝐷 and
measure the size of the angle marked 𝑥.
Now, this is a scale drawing
question. So it’s important that when you
print this out in order to do the question and make the measurements on the page,
you print it with a scale set to 100 percent. Don’t print it scale fit to paper;
otherwise, it will come out the wrong size and you’ll get different answers to what
I’m gonna go through.
And it’s also worth mentioning that
you need to look directly down onto your ruler or your protractor when you’re taking
measurements. If you look directly down, you’ll
accurately be able to read whereabouts the mark on the page is compared to the mark
on your ruler. But if you look at an angle,
because your ruler has a certain thickness, you’ll get something called parallax
error. And it will look like the object on
the page is in a slightly different position through the measurement of the
Okay then, let’s get on with
measuring the length of side 𝐴𝐷 and the measure of this angle 𝑥. Take a bit of time to carefully
place your ruler on the diagram, make sure that the zero line lines up exactly with
one end of the line, and then make a note which millimetre marking matches up with
the other end of the line.
Now, there are 10 little marks
between six centimetres and seven centimetres. Each one represents a
millimetre. And 𝐴 is on the seventh of
those. So that’s seven millimetres. So the distance from 𝐷 to 𝐴 is
six whole centimetres plus seven tenths of a centimetre, in other words 6.7
centimetres. And don’t forget sometimes it’s
easier just to turn the page round in order to look at these measurements on your
ruler. So you’re allowed to do that.
To measure the angle in part b, we
need to line up the base on the protractor — that’s this line here between the zeros
on the protractor — with one of the lines on the diagram and make sure that the
crosshair here lines up with the angle itself, at vertex 𝐵 on our shape.
Take a moment to check carefully
that the baseline is accurate and the crosshair are accurate. Then, you can start counting from
zero and work your way up until you meet the line as we do here. Now, as we’re counting up: zero,
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110. So the answer is the angle marked
𝑥 is 110 degrees.
It is worth pointing out that a
common mistake there might be to read off the other number 70 and write the answer
as 70. Now, clearly, this angle here is
greater than 90 degrees. Here, you can see 90 degrees and
our angle is greater than that.
So that was a just a quick visual
check that the answer wasn’t 70. But the fact that we started at
zero and ran our finger around and counted up along the degrees, along here, that’s
always gonna lead us to the correct answer, in this case 110 degrees.