The first 1-4 questions you have to identify the angles as minor, major, or semicircle. Also you have to find each measure. They give you measure DC which is 80. Then you are left to find ED and AE. You would subtract 180-80 because AEDC are all equal to 180. Then you would get 100 and you have to divide that by 2 and it would be 50. So now you know that AE and ED measure is 50. They give you the measure of BC which is 100. To find AB you have to subtract 180 from 100 because ABC is a semicircle that equals 180. Then you will find that AB is 80. For number one, you have to find AE which is 50 and it is minor because it is less than 180. Number two you have to find AB which is 80 and it is minor because it is less than 180. Number three you have to find EDC which is 130 because you have to add 80+50. Then it would be a minor arc because it is less than 180. Number four you have to find ADC which is 180 because you have to add 50+50+80. It is a semicircle because it is exactly 180.
For number five, you have to find the radius and diameter of a circle with a circumference of 38m. To find the radius you would use the formula of c=d over pi. When you plug in it in you will have c=d times pi. First, you have to divide each side by pi. Then you will have d on the side by itself because the pi will cancel out on one side. So you will have 38 over pi=d. 38 divided by pi equals 12.096 which would be your diameter. To find the radius your formula would be c=2pir. When you plug in your numbers you will have 38=2pir. First you will divide by 2 on each side and 38 divided by 2 is 19. Then, your formula would be 19=pir and you would then divide pi by both sides. When you divide pi on both sides you will get r=6.048 and that is your answer for the radius.
For number 6, they tell you that circle v and w are congruent. You would have to equal 9x-78 to 3x. When you equal to each other then you are able to check if they are equal to each other. First, when you equal them to each other you would subtract 9x from each side and you will get -78= -6x. Then, you would have to divide -6x by -78 and you will get x equals 13. To check if they are equal you will plug 13 into x for each problem. For circle v you have 9(13)-78 and you will get 39. For circle w you have 3(13) which equals 39.
For number 7, you have to find x. So you would equal the two problems that have x in them to each other. You have to equal them to each other because they are congruent to each other. You would equal 3x-23 to 2x+2. First, you will subtract 2x from 3x on the other side and then you will have x-23=2. Then,you would add 23+2 and you will get x=25. To check your problem you would plug in 25 for x. When you sub x for 25 you would get 2(25)+2 and your answer will be 52. When you sub x for 25 you would get 3(25)-23 and your answer would be 52.
For number 8, you have to use the formula for Pythagorean Theorem which is a^2+b^2=c^2. When you plug in your numbers you will have 8^2+x=17^2. You know that 17 is the last number because it is across from you angle which is your hyp. Then you would solve for the squared numbers and you would have 64+x=289. Then you would subtract 289 from 64 an get x^2=225. Then you would have to find the square root of 225. The square root of 225 is 15 and 15 will equal x. So 15 will be your answer.
For number 9, you have to use the formula m<y= 1/2 (mLX – mLW). This formula is for interesting secants and tangents on the exterior. Then you will plug in your numbers and you will have m<y= 1/2 (105-63). First, you have to solve for the parenthesis. So your equation will now be m<y= 1/2(42). Next, you will have to solve 1/2 divided by 42 and that equals m<y=21. So your answer would be 21.
For number 10, you have to use the formula a(a+b)=c(c+d). When you plug in your numbers and you will have 6(6+4x)=6(6+x+3). First, solve the second parenthesis. Then you will have 6(6+4x)=6(9+x) and you will use distributive property. Once you use distributive property your problem would be 36+24x=54+6x. Then ld divide 18 on both sides and get x=1.You would subtract 36 on both sides and you would get 24x=18+6x. Second, you would subtract 6x from both sides and your problem would be 18x=18. Then, you would your answer would be 1.
Alexis Andrews Geometry Blog 