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.

step-by-step explanation:

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5