Prove that the measures of the interior angles of a triangle sum to
180
.
The diagram shows
△
P
Q
R
.
It also shows
segment
P
R
extended through point
S
and
R
T
parallel to
segment
P
Q
.
Complete the proof that
m
∠
P
m
∠
Q
m
∠
Q
R
P
180
.
First,  = 
180
, since those angles form a straight angle. Also, since 
segment
P
Q
R
T
, 
∠
P
 by the Corresponding Angles Theorem and 
∠
Q
∠
Q
R
T
 by the . Now, because the measures of , 
m
∠
P
 =  and 
m
∠
Q
m
∠
Q
R
T
. So, using substitution, 
m
∠
P
m
∠
Q
m
∠
Q
R
P
180
.
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