Question Video: Finding the Measure of Each Angle in a Quadrilateral given a Relation between the Angles’ Measures Mathematics • 8th Grade

Determine the value of 𝑥 in the given quadrilateral.


Video Transcript

Determine the value of 𝑥 in the given quadrilateral.

In the diagram, we can see a quadrilateral. And, of course, quadrilateral means a four-sided shape, one, two, three, four. It looks like it might be a square but we’re not told anything about the measurement of each side. So, we don’t know that for sure.

We can also see that this quadrilateral has four angles. All quadrilaterals have got four angles, but this particular quadrilateral has got four angles that are equal. We know this because they’re all labelled the same way, six 𝑥 degrees. And our problem asks us to determine, or to find, the value of 𝑥 in the quadrilateral.

Now if we were just to use our eyes and to look at this shape, we might say that it looks like each angle is worth 90 degrees. But we don’t know this for sure. Let’s try and prove what each angle’s worth. And then, we can find the value of 𝑥.

To help us solve the problem, we need to remember one fact about angles in a quadrilateral. When we add all the interior angles inside a quadrilateral together, they always make 360 degrees. And the same is true of this shape. So, if we divide 360 by four, we can find the value of one of our angles. Can we think of a number fact that can help us?

Well, we know that 36 divided by four equals nine. 360 is ten times 36, and so the number of fours in 360 will be ten times the number of fours in 36, which is 90. So, we know that each angle inside our shape is actually 90 degrees like we thought. But we’ve proved it using maths. So, we know that each one of our six 𝑥 degrees represents 90 degrees.

Remember, when we use letters alongside numbers like this, six 𝑥 actually means six multiplied by 𝑥, or six lots of 𝑥. 𝑥 just represents a mystery number. So, we can ask ourselves, six times what equals 90? How many sixes are there in 90? We can split 90 into 60 and 30. There are ten sixes in 60. And there are five sixes in 30. So, this means there are 15 sixes in 90. And so, we know the value of 𝑥 equals 15

We’ve found the answer by first remembering a useful fact to help us. All angles inside a quadrilateral add together to make 360 degrees. We then noticed that the four angles inside our quadrilateral were all equal. So, we knew that if we divided 360 by four, we could find the value of one of the angles.

We used a division fact that we already knew to help us. And we found one angle by calculating 360 divided by four. This was 90, so we could say that six 𝑥, or six lots of 𝑥, equals 90 degrees. And so, to find the value of 𝑥, we simply had to find how many sixes there were in 90. 𝑥 has a value of 15.

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