4920 is the numb to nestrest ten
The Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent .Given <A and <B are vertical angles so they are equal.
<A=<B.
Measure of <A=x and <B=5x-80
Or 5x-80=x
Adding 80 both sides
5x-80+80=x+80
5x=x+80
Subtracting x both sides
5x-x=x-x+80
4x=80
Dividing both sides by 4
x=20
Measure of <A= x= 20 degrees.
If you expand out the brackets you get this,
(4+5i)(a+2i) = 4a + (5a)i + 8i - 10
The -10 comes from 5i * 2i.
Squaring i becomes -1.
Let's group the real stuff together,
and imaginary separately,
(4a - 10) + (5a + 8)i
For this to be purely imaginary,
the real part needs to be zero.
Therefore 4a - 10 = 0
Solve for a.
Answer:

Step-by-step explanation:
sec(theta) is defined as: 
In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: 
So this gives us the equation where a=adjacent side:

Subtract 25 from both sides

Take the square root of both sides

So now plug this into the definition of sec(theta) and you get:
. This is in most simplified form since 41, has no factors besides 41 and 1.