Question Video: Finding the Missing Angle in a Given Irregular Polygon | Nagwa Question Video: Finding the Missing Angle in a Given Irregular Polygon | Nagwa

Question Video: Finding the Missing Angle in a Given Irregular Polygon Mathematics • First Year of Preparatory School

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In the diagram below, what is the measure of angle 𝐴𝐵𝐶?

01:50

Video Transcript

We’ve been given a diagram and we’re asked to calculate the measure of angle 𝐴𝐵𝐶.

So that’s this angle here, when I go from 𝐴 to 𝐵 and then to 𝐶. The angle is currently labelled as 𝑦. So we’re going to need our formula for the sum of the interior angles at some stage, so I’ve written that down again here. And let’s look at what we’ve got. If we count the number of sides in the diagram, we have five sides, so 𝑛 is equal to five. So our strategy here, we can work out the total sum of the interior angles by using this formula. We know three of them, so we’ll be able to subtract that. And then the remaining two angles are both labelled as 𝑦, which means they’re the same. So whatever is left over, if we halve it, that will give us the measure of angle 𝐴𝐵𝐶. So let’s go through the working for this.

So the sum of the interior angles is 180 times three. That’s five minus two because there were five sides, which gives us 540 degrees for the total sum. So this means that all of these angles added together, so 121 plus 110 plus 85 plus two lots of 𝑦 must be equal to 540. Now we could write that down as an equation. And now we have this equation, we just need to go through the steps to solve it in order to work out the value of 𝑦. So first of all, if I just combine those 121, 110, and 85 together, so now I have the equation two 𝑦 plus 316 is equal to 540.

The next step to solving this would be to subtract 316 from both sides of the equation, so now I have two 𝑦 is equal to 224. And then to find 𝑦, I can halve both sides of the equation. And that gives me a final answer of 𝑦 is equal to 112 degrees.

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