Question

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

Answer 1

9514 1404 393

Answer:

m∠RPQ = 20°

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°