I need help understanding how to do this problem. Can anyone help me out?

Masterx4020 Oct 2, 2019

#1

#2

#3**+2 **

*I need help understanding how to do this problem. Can anyone help me out?*

I'm going to assume that what looks like a diameter is actually a diameter.

AD is a straight line, which contains 180^{o}

The right angle is 90^{o} plus the 52^{o} totals 142^{o}

Subtract that from the 180^{o} of AD and it leaves 38^{o} for that small sliver of an angle (AB)

Since that angle is 38^{o} then so is the other small sliver on the other side (DE)

Subtract the 38^{o} (DE) from the straight line 180^{o} (AD) and that leaves 142^{o} for AE

Guest Oct 2, 2019

#4**0 **

I did that but when you add up the rest of the arcs it goes past 360 degreees. I don't think it is suppose to do so.

Masterx4020
Oct 2, 2019

#6**+2 **

52+90+38 = 180

142+38 = 180

line BE is 180

when you do the math the angle of 52+90+38=180

so..

The same goes for AD 52+90+38=180

There for 142+38=180

So...

180+180=360

travisio Oct 2, 2019

#8**0 **

I'm not sure about this, because i'm not sure if DA and EB are diameters of the circle or not. If they are, then I can answer.

However, if we assume that EB is the diameter...

Arc EB is 180 degrees (the arc that goes through points D and C).

All together, then angle DOC (where O is the center) + angle BOC + angle EOD = 180

We already have 90+52 which is 142

180-142 = 38

So EOD is 38 degrees.

Now, arc AD is 180 degrees (again assuming that AD is the diameter)

So simply do 180-38 which is 142

So arc EA is 142.

You are very welcome!

:P

CoolStuffYT Oct 2, 2019

#10**+1 **

Thank you everyone who helped me. I understand it now. I have another question I am struggleing with and it is this one.

IT wants me to find angle LPN. How do I Get the angles on inside the quadraltiral? Thanks again.

Masterx4020 Oct 2, 2019

#15**0 **

Here's something that you need to know to solve this problem: It's a Cyclic Quadrilateral.

Cyclic Quadrilaterals are basically quadrilaterals that can be inscribed in a circle.

In Cyclic Quadrilateral LMNP, angle L + angle N = 180, and angle M + angle P = 180. That's just the property of one.

Angle M = arc LP + arc NP / 2, or 123 degrees.

So angle P = 180-123 = 57 degrees.

You are very welcome!

:P

CoolStuffYT
Oct 2, 2019