Question

If in an Isosceles triangle one angle is $70°$ then which of the following statements are correct?

• A. $\left(1\right)$ only
• B. $\left(2\right)$ only
• C. $\left(3\right)$ only
• D. $\left(1\right)$ and $\left(2\right)$ only

Answer 1

The correct option is D

$\left(1\right)$ and $\left(2\right)$ only

Explanation for the correct option:

Step $1$: Let $70°$ is the base angle.

Since the give triangle is Isosceles triangle and angles corresponding to equal sides are equal. Let the angle be $\mathrm{x}°$.

We know that sum of all the angles in a triangle is $180°$.

$\begin{array}{cc}\Rightarrow & 70+x+x=180\\ \Rightarrow & x=55°\end{array}$

So both the angles are $55°$.

Step $2$: Let $70°$ is not the base angle.

Since the give triangle is Isosceles triangle and angles corresponding to equal sides are equal. Thus the two angles will be $70°$.

Let the base angle be $\mathrm{x}°$.

We know that sum of all the angles in a triangle is $180°$.

$\begin{array}{cc}\Rightarrow & 70+70+x=180\\ \Rightarrow & x=40°\end{array}$

Hence, option $\left(D\right)$ is the correct option.