Question

Two triangles DEF and GHK are such that $\angle D={48}^{o}and\angle H={57}^o$. If $\Delta DEF\sim \Delta GHK$ then find the measure of $\angle F$.

Answer 1

In two triangles are similar then the corresponding angles of the two triangles are equal.

Here, $\Delta DEF\sim \Delta GHK$

Therefore, $\angle E=\angle H={57}^o$

Now, in $\Delta DEF$

$\angle D+\angle E+\angle F={180}^o$ (Angle sum property of triangle)

⇒ $\angle F={180}^o–{48}^o–{57}^o={75}^o$
$\angle F={75}^o$