In this diagram, EA−→−⊥ ED−→− and EB−→− bisects ∠AEC . Given that m∠AEB = 4x + 1 and m∠CED = 3x, determine the missing measures.

Hey!

I hope you don't mind, but before I answer this question I'd like to do a quick review of some general angles and how to tell which is which.

QUICK REVIEW

So, let's first review what an acute angle is. An acute angle is an angle that is smaller than 90°. The word acute basically means having a sharp or pointy end. So this is a helpful way to remember what an acute angle is.

Now, let's review what an obtuse angle is. An obtuse angle is an angle that is more than 90°. If an angle measures over 90° that it is more than likely that it is an obtuse angle.

Last but not least a right angle. A right angle is an angle that has to be exactly 90°. If an angle is 90° than it is most definitely a right 

END QUICK REVIEW

Let's start by finding out the angle in the top left hand corner. The angle is clearly no more that 90° and is not 90° exactly. This angle must be an acute angle. We can also tell that it is an acute angle because the angle is sharp.

Now let's look at the angle on the bottom left hand corner. The angle is clearly no less than 90° and more than 90° exactly. This angle must be an obtuse angle.

Since the angles are basically the same on the other side, we won't be reviewing those. Now we'll count all the angles we have.

Acute Angles - 2

Obtuse Angles - 2

Right Angles - 0

So, this means that in the figure shown above,  there are 2 acute angles, 2 obtuse angles, and no right angles.

Hope this helps!

- Lindsey Frazier ♥