Question

are these triangles similar?
triangle kij with angle at k: 52°, angle at i: 84°; triangle fgh with angle at f: 84°, angle at h: 55°.
options: yes, no

Explanation:

Step1: Find missing angle in $\triangle JKI$

Sum of angles in triangle is $180^\circ$.
$\angle J = 180^\circ - 52^\circ - 84^\circ = 44^\circ$

Step2: Find missing angle in $\triangle FGH$

Sum of angles in triangle is $180^\circ$.
$\angle G = 180^\circ - 84^\circ - 55^\circ = 41^\circ$

Step3: Compare angle sets

$\triangle JKI$ angles: $44^\circ, 52^\circ, 84^\circ$
$\triangle FGH$ angles: $41^\circ, 55^\circ, 84^\circ$
No matching pair of two equal angles.

Answer:

no