Question

In an isosceles triangle, one angle is $$70^{o}$$. The other two angles are of
(i) $$55^{o}$$ and $$55^{o}$$
(ii) $$70^{o}$$ and $$40^{o}$$
(iii) any measure
In the given option(s) which of the above statements(s) are true?

Answer 1

Correct option is D. (i) and (ii)
Case II: Here, triangle $$ABC$$ is an isosceles triangle.
$$AB=AC$$ and vertex angle $$=70^{o}$$
$$\angle 1=\angle 2 \, \, \,...(1)\because AB=AC$$
Now,
$$\angle 1+\angle 2+\angle A=180^{o}$$
$$\Rightarrow 2(\angle 1)=180^{o}-70^{o}$$
$$\Rightarrow \angle 1=\dfrac{110^{o}}{2}=55^{o}$$
Therefore, $$\angle 1= \angle 2=55^{o}$$
In above Figure, Triangle ABC is an isosceles triangle
$$AB=AC$$, Base angle $$=\angle 2=70^{o}$$
$$\angle 1+\angle 2+\angle C=180^{o}$$
$$\Rightarrow \angle 1=180^{o}-70^{o}-70^{o}$$
$$\Rightarrow \angle 1=40^{o}$$
Therefore, $$\angle 1=40^{o}, \angle 2=70^{o}$$
Both statements are true.