A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. A regular pentagon is shown. Lines are drawn from each point to a point in the center to form congruent isosceles triangles. The lengths of all lines are congruent. The total number of degrees of all center angles is 360 degrees. The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles?

Each base angle of one triangle is 54°

Step-by-step explanation:

Since the angles meeting in the center are congruent and all form 360° then it means each angle will be 360°/5 = 72°(since we have 5 angles).

Since they are all isosceles triangles, it means two base angles are equal and can be gotten by:

(180 – 72)/2 = 54°.

Each base angle of one triangle is 54°

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.