Given that lines marked with arrows in figure 10.36 are parallel, determine the sum of the angles a+b+c+d+e without measuring the angles. explain your reasoning

a + b + c + d + e = 180.

Step-by-step explanation:

We can prove that a = angle CBA (vertically opposite angles are equal).

Now, since lines DE and CA are parallel, then it follows that c = angle ACE (alternate angles are equal). Similarly, b = angle CAD.

But notice that what we've just done is found the angles of the triangle CBA.

So the sum of the angles (a + b + c + d + e) is the sum of the angles of a triangle.

We then conclude that a + b + c + d + e = 180 degrees.

hi there!

the answer will be d: 2

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.