Question

Question 2

$\Delta DEF$ in the given figure is a right-angled triangle with $\angle E={90}^{\circ }$. What type of angles are $\angle D$ and $\angle F$?

a) They are equal angles
b) They form a pair of adjacent angles
c) They are complementary angles
d) They are supplementary angles

Answer 1

Since, $\angle D,\angle Eand\angle F$ are angles of a triangle
So in $\Delta DEF$,
$\angle D+\angle E+\angle F={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow \angle D+{90}^{\circ }+\angle F={180}^{\circ }$ $[\because \angle E={90}^{\circ },given]$
$\Rightarrow \angle D+\angle F={180}^{\circ }-{90}^{\circ }\Rightarrow \angle D+\angle F={90}^{\circ }$

Hence, $\angle Dand\angle F$ are complementary angles.