Question

determine if triangle opq and triangle rst are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
two triangles are shown: triangle opq with angles at p (82°), o (49°); triangle rst with angles at r (49°), t (49°)
answer
attempt 2 out of 2
the triangles dropdown similar.

Explanation:

Step1: Find ∠Q in △OPQ

Sum of angles in a triangle is $180^\circ$.
$\angle Q = 180^\circ - 82^\circ - 49^\circ = 49^\circ$

Step2: List angles of both triangles

△OPQ: $\angle O=49^\circ$, $\angle P=82^\circ$, $\angle Q=49^\circ$
△RST: $\angle T=49^\circ$, $\angle R=49^\circ$, $\angle S=180^\circ - 49^\circ - 49^\circ=82^\circ$

Step3: Match corresponding angles

All three pairs of corresponding angles are equal:
$\angle O = \angle T = 49^\circ$, $\angle P = \angle S = 82^\circ$, $\angle Q = \angle R = 49^\circ$
By AA (Angle-Angle) similarity criterion, the triangles are similar.

Answer:

The triangles are similar. We know this because all corresponding angles of the two triangles are equal, satisfying the AA (Angle-Angle) similarity postulate.