The ratio of two complementary angles is 8:17. find the measure of the smallest angle.

Let's assume that the two angles represent
x
and
y
. We know that
x
+
y
=
90
. For this equation, let's assume
y
is the bigger angle.
y
would equal 8:7x, or to make it simpler,
8
7
x
. We can plug in
8
7
x
for
y
in the original equation to get
x
+
8
7
x
=
90
. Combining like terms, and then saying that
x
=
7
7
, we get
15
7
x
=
90
. We then divide
15
7
on both sides, and get
x
=
42
. In the equation,
y
=
8
7
x
, we add in 42 which makes
y
=
48
. That's how we find out our answer.