Here is the more clearer picture

angle FDA = 75 degrees

angle JAI = 75 degrees

Step-by-step explanation:

In ΔDCE,

angle D + angle C + angle E = 180(sum of the interior angles of a triangle is always 180 degrees)

angle D + 80 + 25 = 180

angle D + 105 = 180

angle D = 180 - 105

angle D (I. e angle CDE ) = 75 degrees

Now, angle CDE and angle FDA are vertically opposite angles, so,

angle CDE = angle FDA (vertically opposite angles are congruent to each other)

therefore, angle FDA = 75 degrees

Now, angle CDE and angle BAD are corresponding angles, so,

angle CDE = angle BAD ( corresponding angles are congruent to each other)

angle BAD = 75 degrees

Now, angle BAD and angle JAI are vertically opposite angles, so,

angle BAD = angle JAI (vertically opposite angles are congruent to each other)

therefore, angle JAI = 75 degrees

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

divide the numbers

step-by-step explanation: