Question

If the supplement of an angle is three times its complement ; find both the angles

Answer 1

let that angle be x
180-x = 3(90-x)
180 - x = 270 - 3x
2x=90
x=45°
so its complement is 45° and its supplement is 135°

Answer 2

Let the angle be x
Then ,
90
−
∠
x
be the complement
180
−
∠
x
be the supplement
180
−
∠
x
=
3
(
90
−
∠
x
)
+
20

180
−
∠
x
=
270
−
3
∠
x
+
20

180
−
∠
x
=
290
−
3
∠
x

−
110
=
−
2
∠
x

55
∘
=
∠
x