Two lines intersect at a point. the vertical angles formed are supplementary.

we know that

Vertical angles are a pair of opposite and congruent angles formed by intersecting lines.

so

Let

x1> angle vertical 1

x2> angle vertical 2

x1=x2 > equation 1

in this problem

if the vertical angles formed are supplementary

that means that

x1+x2=180 > equation 2

substitute equation 1 in equation 2

x1+x1=180

2x1=180

x1=180/2

x1=90 degrees

therefore

the answer is

The vertical angles are right angles

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for