Question

The interior angles of △ABC measure 34°, 50°, and x°. The interior angles of △DEF measure y°, 50°, and 96°. Which statement is true? The triangles are not similar because x≠y . The triangles are similar because y=34 and there are three pairs of congruent angles. The triangles are not similar because y≠34 . The triangles are similar because they each have an interior angle that measures 50°.

Answer 1

we know that

The sum of the internal angles of a triangle must be
`180` degrees

Step
`1`

Find the measure of the angle x in the triangle ABC

`34+50+x=180\\84+x=180\\x=180-84\\x= 96\°`

Step
`2`

Find the measure of the angle y in the triangle DEF

`y+50+96=180\\y+146=180\\y=180-146\\y= 34\°`

so

The measure of the angles in the triangle ABC are
`34,50,96`

The measure of the angles in the triangle DEF are
`50,96,34`

so

The triangles are similar because there are three pairs of congruent angles

Statements

1) The triangles are not similar because x≠y --------> Is false

2) The triangles are similar because y=34 and there are three pairs of congruent angles--------> Is true

3) The triangles are not similar because y≠34--------> Is false

4) The triangles are similar because they each have an interior angle that measures 50°------> Is false

Answer 2

according to the triangles similarity properties, The triangles are similar because y=34 and there are three pairs of congruent angles
x° must be equal 96°