Question

Two triangles DEF and GHK are such that ∠D = 48° and ∠H = 57°. If ΔDEF ∼ ΔGHK then find the measures of ∠F.

Answer 1

If two triangles are similar then the corresponding angles of the two triangles are equal. Here, ΔDEF ~ ΔGHK  

∴ ∠E=∠H=57° 

Now, In Δ DEF 

∠D+∠E+∠F180°      (𝐴𝑛𝑔𝑙𝑒 𝑠𝑢𝑚 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒) 

⇒ ∠F=180° -48° -57° =75°