Question

In a triangle, one angle is of $90°$. Then

(i) The other two angles are of $45°$ each.

(ii) In remaining two angles, one angle is $90°$ and other is $45°$.

(iii) Remaining two angles are complementary.

In the given option(s) which is true?

• A. $\left(i\right)$ Only
• B. $\left(ii\right)$ Only
• C. $\left(iii\right)$ only
• D. $\left(i\right)$ and $\left(ii\right)$

Answer 1

The correct option is C

$\left(iii\right)$ only

Step 1: Explanation for the correct option:

Option $C:$ $\left(iii\right)$ only.

According to the angle sum property of a triangle, the sum of all the angles of any triangle is equal to $180°$.

Since it is given that one angle is of $90°$. That means the sum of the other two angles will be $90°$.

Assume that, one of these two angles is $x$.

Therefore, the other ($3^{rd}$) angle will be $90°-x$.

So, the remaining two angles are complementary angles.

Hence, option $C$ is the correct option.

Step 2 : Explanation for the incorrect option:

Option $A:$ $\left(i\right)$ only.

Statement $\left(i\right):$The other two angles are of $45°$ each.

Since Statement $\left(i\right)$ satisfy the angle sum property of the triangles but it is a particular case and it is not compulsory that is one angle of the triangle then the other two angles are of $45°$ each.

Hence, option $A$ is the incorrect option.

Option $B:$ $\left(ii\right)$ only.

Statement $\left(ii\right):$ In the remaining two angles, one angle is $90°$ and other is $45°$.

Since statement $\left(ii\right)$ does not satisfy the angle sum property of triangle.

Therefore, option $B$ is the incorrect option.

Hence, option $C$ is the only correct answer.