Answer:
135°
Step-by-step Explanation:
==>Given:
An inscribed quadrilateral ABCD with,
m<A = (3x +6)°
m<C = (x + 2)°
==>Required:
measure of angle A
==>Solution:
First, let's find the value of x.
Recall that the opposite angles in any inscribed quadrilateral in a circle are supplementary.
Therefore, this means m<A + m<C = 180°
Thus, (3x+6) + (x+2} = 180
3x + 6 + x + 2 = 180
Collect like terms:
3x + x + 6 + 2 = 180
4x + 8 = 180
Subtract 8 from both sides:
4x + 8 - 8 = 180 - 8
4x = 172
Divide both sides by 4:
4x/4 = 172/4
x = 43
We can now find m<A = (3x + 6)°
m<A = 3(43) + 6
= 129 + 6
measure of angle A = 135°
Answer:
C. 108
Step-by-step explanation:
The angles are known as same-side interior angles. They are supplementary angles so their sum is 180°.
First, do 40 - 12 = 28 (Subtract the change), then do 28 / 7 to get 4, so then we do the cans times 3 to see how many individual balls he has, which would be 12
Answer:
7
Step-by-step explanation:
Answer: 10
Imagine you have 2 slots or boxes that are empty. They represent the possible choices for the letter you pick. For example, you can place B in slot 1 and D in slot 2. There are 5 choices for slot 1 (A,B,C,D,E) and four choices for slot 2. Why 4? Because after we pick the letter for slot 1, we have one less letter to pick from. We can't reuse that letter.
Now multiply those values 5 and 4 to get 20. There are 20 different ways to pick a pair of letters from a pool of 5 total. However, order does NOT matter because the segment AB is the same as BA. Since order doesn't matter, we are doubly counting when we shouldn't. In other words, our count is two times higher than it should be. Instead of 20 pairs, it's actually 20/2 = 10 pairs. That's why the answer is 10.
The list of 10 segments are: {AB,AC,AD,AE,BC,BD,BE,CD,CE,DE}
Side note: you can use the nCr combination formula with n = 5 and r = 2 to get the same answer.
