Angle abc is formed by segments ab and bc on the coordinate grid below: a coordinate plane is shown. angle abc has vertices at 3 comma 4 and 5 comma 3 and 3 comma 2 and measures 53.13 degrees. angle abc is rotated 90 degrees counterclockwise about the origin to form angle a′b′c′. which statement shows the measure of angle a′b′c′? m∠a′b′c′ = 90 degrees m∠a′b′c′ = 180 degrees m∠a′b′c′ = m∠abc m∠a′b′c′ = 2 × m∠abc

m∠ABC = m∠A'B'C'

Step-by-step explanation:

We are given a ΔABC with the co-ordinates ( 3,4 ), ( 5,3 ) and ( 3,2 ) along with ∠ABC = 53.13°

Now, it is given that ΔABC is rotated counter-clockwise by 90° to make the  ΔA'B'C'.

So, we get a new triangle having co-ordinates ( -4,3 ), ( -3,5 ) and ( -2,3 ).

Since, rotation is a transformation that does not change the side length or the angle measure i.e. it preserves the congruence.

So, we get that ∠A'B'C' = 53.13°

Hence, ∠ABC = ∠A'B'C' = 53.13° i.e. m∠ABC = m∠A'B'C'

, 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

y/x of point b= y/x of point a

step-by-step explanation:

(i got the same question, this was the correct answer.)