Answer:
Option D is correct.
No, the triangles are not similar.
Step-by-step explanation:
AA postulates states that two triangles are similar if they have two corresponding angles equal.
Labelled the diagram as shown below:
We know that sum of all the measure of the angles in a triangle is 180 degree.
In triangle ABC:
[tex]\angle A + \angle B + \angle C = 180^{\circ}[/tex]
⇒[tex]30.4^{\circ}+84.6^{\circ}+\angle C = 180^{\circ}[/tex]
⇒[tex]115^{\circ}+\angle C = 180^{\circ}[/tex]
Subtract 115 degree from both sides we get;
⇒[tex]\angle C = 65^{\circ}[/tex]
In triangle ABC and PQR
[tex]\angle A = \angle Q = 84.6^{\circ}[/tex]
[tex]\angle C \neq \angle R[/tex]
i.e [tex]65^{\circ}\neq 66^{\circ}[/tex]
⇒These triangles does not satisfy the AA postulates
Therefore, the given triangles are not similar.
