Answer:
(d) The triangles are similar, because each has angles that measure 36°, 62°, and 82°.
Explanation:
Given triangle A has angles 36° and 82°, and a figure showing angles related to triangle B, you want to know if the triangles are similar.
Similarity
The triangles will be similar if the angles of one are congruent to the angles of the other. Between the two triangles, we are given 3 different angle values, so we need to find at least two additional angle values in order to determine if the triangles are similar.
Angle sum theorem
The sum of angles in a triangle is 180°, so the third angle of triangle A will be ...
angle = 180° -36° -82° = 62°
Exterior angle
The exterior angle of triangle B, given as 144°, is the sum of the remote interior angles:
144° = 62° +angle
82° = angle
Comparison
Now, we have the angles of triangle A as 36°, 62°, and 82°. Two of the angles of triangle B are known to be 62° and 82°, matching those of triangle A.
The triangles are similar, because each has angles that measure 36°, 62°, and 82°.