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

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?

Dawn is selling her mp3 player for 3 4 of the original price. the original price for the mp3 player was $40. how much is she selling her mp3 player for?