Math Is Fun Forum

1. I know this one is relatively easy, I just cannot for the life of me remember these tricky angle rules, so please help.
In the diagram shown, parallel lines m and n are cut by transversal p.
https://i.imgur.com/ScllcCF.png
Which statement about angle 1 and angle 2 must be true?
A) Angle 1 ≅ Angle 2
B) Angle 1 is the complement of Angle 2
C) Angle 1 is the supplement of Angle 2
D) Angle 1 and Angle 2 are vertical angles

2. What is the value of x in this diagram?
https://i.imgur.com/Mpokyjc.png
A) 60 deg
B) 72 deg
C) 90 deg
D) 120 deg

Thanks!

Hello, I gotta find the areas of these two shapes, but I'm having a ton of trouble. I just can't figure out where to start. Can someone give me some pointers, please? Thanks.

#1: https://i.imgur.com/4PIIUjw.png
#2: https://i.imgur.com/rdP6UPM.png

Please help me out with this question.

My mom made a round cake with a 10 inch radius. She cut the cake into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the icing more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain less icing, and the outer piece would contain the icing.

https://i.imgur.com/yQ2zLKX.png

1. Find the area of the whole cake.
A: π x 102^2. The area is 314.16

2. What is the area of one piece of cake?
A: I'm not sure what's being asked. Since the cake is split into 16 pieces, you just divide 314.16 by 16, right? That gives 19.635.

3. What is the area of a half-piece?
A: Half of a piece is 19.635 divided by 2? I'm not sure. That gives 9.8175.

4. What would the area of the whole cake be if it were cut into half pieces?
A: Not sure what's being asked.

5. What is the radius of a half-piece when it is cut as shown in the picture? (ie, where do I need to cut to make two equal halves out of a piece?)
A: ∑（´△｀○）I have no idea.

Thank you!

https://i.imgur.com/aLAIl5k.png

You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between the tree and the line of sight to your red lunchbox is 30°. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree?

A. 75.36 m
B. 92.09 m
C. 20.17 m
D. 51.25 m
E. 18.95 m
F. 34.64 m

The last question!! Please help, I'd love to get this done as quickly as I can. Thank you!!

An angle "p" exists that is complementary to angle g on one side. On the other side, the angle p is supplementary to angle h. The sum of the three angles is 200°. What is the measure of this common angle p? (Show your work AND upload a drawing of this problem.)

So, p + g = 90
p + h = 180
p + g + h = 200?
Where in the world do I start with this? And the drawing? Aggghhh. I'm really not good with angles.

I need help with 2 questions, please.
Here's the angle:

The questions are:
In the figure linked, is AB is parallel to CD...
1. If angle 5 = 30° and angle 3 = 150°?
A. Yes because angles 5 and 3 are same-side interior angles.
B. Yes because angles 5 and 3 are alternate interior angles
C. Yes because angles 5 and 3 are vertical angles.
D. No because angles 5 and 3 are vertical angles.
E. No because angles 5 and 3 are corresponding angles.
F. No because angles 5 and 3 are alternate interior angles

2. If angle 4 = 80° and angle 6 = 100°?
A. Yes because angles 4 and 6 are vertical angles.
B. Yes because angles 4 and 6 are same-side interior angles.
C. Yes because angles 4 and 6 are corresponding angles.
D. No because angles 4 and 6 are vertical angles.
E. No because angles 4 and 6 are alternate interior angles.
F. No because angles 4 and 6 are alternate exterior angles.

I'm pretty sure both answers are one of the "no"s, but I'm not sure of the reason.

Problem: A cat has thirteen kittens. Eight of the kittens have white hair, six of the kittens have spots, and eight of the kittens have long tails. All of the kittens have at least one of these traits. One kitten is white with spots and a long tail. Three of the kittens are white with spots. Two kittens have spots and long tails. One kitten has white hair but does not have spots or a long tail.

a. Draw a Venn diagram for this problem.
b. How many kittens are white with long tails, but don't have spots?
My answer is 3.

I'm having a hard time wrapping my dull head around this one. So far, I have:
https://i.imgur.com/HrIVYmE.png

But it adds up to 12, not 13. I definitely have something wrong with the spots cats, it can't surely be 0 (maybe?), but it says 6 cats with spots and 3 + 1 + 2 = 6 which leaves no room for cats with just spots.

Please help me out, thanks.