Question

Question 6

In a triangle, one angle is of ${90}^{\circ }$. Then,

i) The other two angles are ${45}^{\circ }$ each.
ii) In remaining two angles, one angle is ${90}^{\circ }$ and other is ${45}^{\circ }$
iii) Remaining two angles are complementary

In the given option(s) which is true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Answer 1

Let us take a right angled triangle $\Delta ABC$,
$\angle B={90}^{\circ }$

As we know,
$\angle A+\angle B+\angle C={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow \angle A+{90}^{\circ }+\angle C={180}^{\circ }\Rightarrow \angle A+\angle C={180}^{\circ }-{90}^{\circ }={90}^{\circ }$
Hence, remaining two angles are complementary.
Hence option(i) and (iii) are correct.