What is next term in sequence 54,-18,6

-2

Step-by-step explanation:

This is a geometric sequence.  We need to find the common ratio

Take the second term and divide by the first

-18/54 = -1/3

Take the third term and divide by the second

-18/6 = -1/3

The common ratio is -1/3

The next term is the third term times the common ratio

6 * -1/3 = -2

The fourth term  is -2

Part 1)
we know that
the property of cyclic quadrilaterals for which opposite angles are supplementary
then
m∠A°+43°=180°> m∠A=180°-43°=137°

the answer is m∠A=137°

Part 2) Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?

we know that
the property of cyclic quadrilaterals for which opposite angles are supplementary
then:
m∠A+m∠C=180∘
(2x+9)+(3x+1)=180> 5x+10=180
x=(180-10)/5=34

m∠A=2x+9> 2*34+9=77°

the answer is m∠A=77°