one angle is 3x-3
another angle is 6(x-10)
Both angles are vertically opposite angles
Vertically opposite angles are always equal
So we equation both the angles and solve for x
3x - 3= 6(x-10)
3x - 3 = 6x - 60
Subtract 6x from both sides
-3x - 3 = -60
Add 3 on both sides
-3x = -57
Divide by 3
x = 19
The value of x= 19
In 22, you're looking for the vertical height of the triangle. You're given the angle opposite the side you want to find (which I'll call

) and the length of the hypotenuse. This sets you up with the relation

In 23, you're given a similar situation, except now you're looking for the angle (I'll call it

) in the triangle opposite the side denoting the height of the airplane. So this time,
Answer:

Step-by-step explanation:
We can prove that a tangent will always be perpendicular to the radius touching it. So, the other angle in the diagram is
.
Because all the angles of a triangle sum to
, we have that
.
We combine like terms on the left side to get
.
We subtract
on both sides to get
.
So,
and we're done!
Answer:
The number of wreaths Alaina sells is 9 .
Step-by-step explanation:
As given
Alaina is selling wreaths and poinsettias for her chorus fundraiser.
Wreaths cost $27 each poinsettia cost $20 each.
If she sold 15 poinsettias and made $543.
Let us assume that the number of wreaths Alaina sells = x
As the number of poinsettias Alaina sells = 15
Than the equation becomes
27x + 15 × 20 = 543
27x + 300 = 543
27x = 543 - 300
27x = 243

x = 9
Therefore the number of wreaths Alaina sells is 9 .