The vertex angle of an isosceles triangle is 42 more than 3 times the base angles. Find the vertex angle. a The vertex angle is 124.8°.

b The vertex angle is 27.6°.

c The vertex angle is 40.8°.

d The vertex angle is 82.8°.

a

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

let x be the base angles, then vertex angle is 3x + 42

Sum the 3 angles and equate to 180, that is

x + x + 3x + 42 = 180

5x + 42 = 180 ( subtract 42 from both sides )

5x = 138 ( divide both sides by 5 )

x = 27.6

Thus

vertex angle = 3x + 42 = 3(27.6) + 42 = 82.8 + 42 = 124.8° → a

, 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