2. The measure of the exterior angle of a triangle is 117° and
one of the remote interior angle measures 79º. Find the
measure of the other remote interior angle
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x + y + z = 180
w + z = 180
x + y + z = 180 (this is the first equation)
w + z = 180 (this is the second equation)
Now, rewrite the second equation as z = 180 - w and substitute that for z in the first equation:
x + y + (180 - w) = 180
x + y - w = 0
x + y = w
exterior angle = interior angle + other interior angle
(
3
x
−
10
)
=
(
25
)
+
(
x
+
15
)
(3x−10)=(25)+(x+15)
3
x
−
10
=
x
+
40
3x−10=x+40
3
x
=
x
+
50
3x=x+50
2
x
=
50
2x=50
x
=
25
x=25
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