Question

Consider the two triangles, which are not drawn to scaleFor the two triangles to be similar by angle-angle similarity, which values could be x be?A. 27 or 115B. 38 or 77C. 52 or 77D. 115 or 153

Answer 1

Recall that the Angle-Angle criterion states that two triangles are similar if two of their angles are congruent.

Now, recall that the interior angles of a triangle add up to 180 degrees, therefore, the other side of the largest triangle has measure

$180^{\circ}-115^{\circ}-38^{\circ}=27^{\circ}.$

Therefore, the values that x could be are:

$27\text{ or 115.}$

Answer: First option.

$27\text{ or 115.}$