The sum of the measures of the angles below is 180∘. A triangle is shown. The first angle measures x degrees. The second angle measures two x minus ten degrees. The third angle measures x plus ten degrees. What is the measure of each angle? Write and solve an equation.

First Angle: 45 degrees, Second Angle: 80 degrees, Third Angle 55 degrees

Step-by-step explanation:

180∘= x+ 2x-10∘+ x+10

180∘=4x

x=45∘

2x-10=80∘

x+10=55∘

, 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

3

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3