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°.

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°

Answer Link

calculista calculista · Answer 2 · 2018-09-26T11:36:03-04:00

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