Two triangles are sketched on a coordinate plane using a dilation of 2, sharing the same center ordered pair at the origin. One triangle has angle measures of 34 degrees and 80 degrees. Using the AA criterion, what would be the two corresponding angles of the dilated triangle?(1 point)

Question

Responses

34 degrees and 80 degrees
34 degrees and 80 degrees

17 degrees and 40 degrees
17 degrees and 40 degrees

44 degrees and 70 degrees
44 degrees and 70 degrees

68 degrees and 160 degrees

Answer 1

The AA (Angle-Angle) criterion states that if two triangles have two angles that are equal, then the triangles are similar.

In this case, since the triangle is dilated, the angles of the original triangle remain unchanged. The dilation affects the side lengths but not the angles.

Given that one triangle has angles of 34 degrees and 80 degrees, the third angle can be calculated as follows:

1. The sum of the angles in a triangle is 180 degrees.
2. The third angle = 180 - (34 + 80) = 180 - 114 = 66 degrees.

Thus, the original triangle has angle measures of 34 degrees, 80 degrees, and 66 degrees.

Since the dilated triangle is similar to the original triangle (as dilation maintains angle measures), the corresponding angles of the dilated triangle are also 34 degrees, 80 degrees, and 66 degrees.

From the responses provided, the correct answer is:

34 degrees and 80 degrees.