Decomposing angles | Math | 4th grade | Khan Academy

What is the measure of angle EAC?

So, we have this symbol here which means angle and then these three letters: E, A, C.

Now, to measure angle EAC, we need to first find angle EAC down here on our picture. The way we can do that is use these three letters, and we're going to go in the order that they're given to us.

So, the first letter we're told is E; the first letter we'll find down here is E. From there, we'll go to the second letter, A, and then finally, from A, we go to our last letter, C. Again, in the order that they were told to us.

So, this opening right here is our angle. We want to know how many degrees this opening is. The most common way to measure an angle would be to use a protractor, but we're not given a protractor, so we can't do that.

But we do have enough information on this diagram down here to solve this. What we can see is that our large angle EAC is made up of two smaller angles. This first one, angle EAD right here, angle EAD plus, from there, it picks up with angle DAC, angle DAC.

These two angles, this first one from here to here and then the second from here to here, when they're combined, they make the same size opening as our angle. So, if we can combine these two angles, we will know the measure of our angle because, again, these two combined are equal to our entire angle.

So, let's do that, starting with EAD. We can see we're told it's 60 degrees; that's a 60-degree opening. Plus, angle DAC has a 75-degree opening.

So, if we combine that, if we go 60 degrees to here plus another 75 down to here, we've covered our entire angle. Our entire opening is 60 plus another 75.

So, we can add these to solve for the measure of our angle. Six tens plus seven tens is thirteen tens or 130. Thirteen and then that zero is there because we're talking about tens. Plus zero ones and five ones is five ones.

So, 130 plus 5 is 135 degrees. Thus, the measure of our entire angle, angle EAC, is 135 degrees.