Question

are these triangles similar?
options: yes, no

Explanation:

Step1: Find missing angle in △QRS

Sum of angles in triangle is $180^\circ$.
$\angle S = 180^\circ - 99^\circ - 51^\circ = 30^\circ$

Step2: Find missing angle in △UVW

Sum of angles in triangle is $180^\circ$.
$\angle W = 180^\circ - 90^\circ - 51^\circ = 39^\circ$

Step3: Compare all angle sets

△QRS angles: $30^\circ, 51^\circ, 99^\circ$
△UVW angles: $39^\circ, 51^\circ, 90^\circ$
No matching 3-angle pairs, so triangles are not similar. Wait correction:
Wait Step1 recalculate: $180 - 99 -51 = 30$, correct. Step2: $180-90-51=39$, correct. The only common angle is $51^\circ$, but all three angles must match for AA similarity. So the correct answer is no.

Corrected Answer:

no

Step1: Calculate ∠S in △QRS

$\angle S = 180^\circ - 99^\circ - 51^\circ = 30^\circ$

Step2: Calculate ∠W in △UVW

$\angle W = 180^\circ - 90^\circ - 51^\circ = 39^\circ$

Step3: Compare angle sets

△QRS: $30^\circ, 51^\circ, 99^\circ$
△UVW: $39^\circ, 51^\circ, 90^\circ$
No three matching angles, so triangles are not similar.

Answer:

yes