In ΔPQR, P
R
‾
PR
is extended through point R to point S,
m
∠
Q
R
S
=
(
7
x
+
8
)
∘
m∠QRS=(7x+8)
∘
,
m
∠
R
P
Q
=
(
x
+
12
)
∘
m∠RPQ=(x+12)
∘
, and
m
∠
P
Q
R
=
(
3
x
+
20
)
∘
m∠PQR=(3x+20)
∘
. Find
m
∠
R
P
Q
.
m∠RPQ

9514 1404 393

  m∠RPQ = 20°

Step-by-step explanation:

Exterior angle QRS is equal to the sum of interior angles RPQ and PQR.

  7x +8 = (x +12) +(3x +20)

  3x = 24 . . . . . . . . . . . . . . . . . . subtract 4x+8

  x = 8

  m∠RPQ = (x+12)° = (8+12)°

  m∠RPQ = 20°

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.