WEBVTT
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Find 𝑥 and 𝑦.
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Here we can see that angle 𝑦 is on the inside of the shape.
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And 𝑥 is on the outside of the shape.
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But exactly what shape is this?
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Since it has eight sides, this will be an octagon.
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So how would we go about finding an interior angle of this octagon and an exterior angle of this octagon?
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Together, these angles make a straight line.
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So together, they add to 180 degrees.
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So if we can find one of them, we can subtract it from 180 and find the other.
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Since 𝑦 is on the inside of this octagon, we can use some things from the octagon to help us find it.
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So let’s begin by finding 𝑦.
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A way that we can find an interior angle is using triangles.
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So how many triangles could fit inside this octagon?
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Here’s one, two, three, four, five, and six, so six total triangles.
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Now how many degrees are in a triangle?
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180 degrees.
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And notice every angle of the triangles create all of the interior angles of the octagon.
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So all of the angles together make the octagon.
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So we can take all six triangles and multiply by 180 degrees because that’s how many degrees are in a triangle.
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And then we get the total in degrees of the interior angles.
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So six times 180 is 1080.
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So that means all of these interior angles add to be a total of 1080.
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So if we just want one of them, we need to divide by eight because there are eight angles in this octagon.
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So we get 135 degrees.
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So angle 𝑦 is equal to 135 degrees.
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And like we said before, angle 𝑥 and 𝑦 make a straight line just 180 degrees.
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So if we can plug in 135 for 𝑦, we can solve for 𝑥.
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So let’s go ahead and subtract 135 from both sides of the equation.
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And we get that angle 𝑥 is equal to 45 degrees.
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So once again, 𝑥 is equal to 45 degrees and 𝑦 is equal to 135 degrees.