Question

In $\Delta DEF,\angle D=2p+8^{\circ },\angle E={90}^{\circ }and\angle f=3p+{32}^{\circ }.$ Find the measures of $\angle D$ and $\angle F$ .

Answer 1

$\begin{array}{c}Wehave\\ \angle D=2p+8^{\circ },\\ \angle E={90}^{\circ }\\ and\angle F=3p+{32}^{\circ }\\ Now,In\Delta DEF\\ \angle D+\angle E+\angle F={180}^{\circ }\\ \Rightarrow 2p+8^{\circ }+{90}^{\circ }+3p+{32}^{\circ }={180}^{\circ }\\ \Rightarrow 5p=180-130\\ \Rightarrow 5p=50\\ \therefore p={10}^{\circ }.\\ Hence,\\ \angle D=2p+8^{\circ },\\ =2\left({10}^{\circ }\right)+8\\ =20+8\\ ={28}^{\circ }.\\ and\\ \angle F=3p+{32}^{\circ }\\ =3\left(10\right)+32\\ =30+32\\ ={62}^{\circ }\\ hence,\angle D={28}^{\circ }and\angle F={62}^{\circ }.\end{array}$