Question

Based only on the information given in the diagram, it is guaranteed that

AJKL ~ AWXY.
27°
A
63"
A. True
B. False

Answer 1

True

Explanation:

Given

In JKL, we have:

`\angle J = 27`

`\angle K = 90`

In WXY, we have:

`\angle Y = 63`

`\angle X = 90`

Required

Is JKL ~ WXY?

In both triangles, we already have one similar angle (90)

Next, is to determine the third angles in both triangles.

In JKL

`\angle J + \angle K + \angle L = 180`

We have that:

`\angle J = 27` and
`\angle K = 90`

The expression becomes:

`27 + 90 + \angle L = 180`

`117 + \angle L = 180`

`\angle L = 180-117`

`\angle L = 63`

In WXY

`\angle W + \angle X + \angle Y = 180`

We have that:

`\angle Y = 63` and
`\angle X = 90`

The expression becomes:

`\angle W + 63 + 90 = 180`

`\angle W + 153 = 180`

`\angle W = 180-153`

`\angle W = 27`

The three angles in JKL are:

`\angle J = 27`
`\angle K = 90`
`\angle L = 63`

The three angles in WXY are:

`\angle W = 27`
`\angle X = 90`
`\angle Y = 63`

By comparing the angles, we can conclude that both triangles are similar because of AAA postulate (Angle-Angle-Angle)