Question

In an isosceles triangle, one angle is ${70}^{\circ }$. The other two angles are of

i) ${55}^{\circ }$ and ${55}^{\circ }$
ii) ${70}^{\circ }$ and ${40}^{\circ }$
iii) Any measure

In the given option(s) which of the above statement(s) are true?

• A. (i) only
• B. (ii) only
• C. (iii) only
• D. (i) and (ii)

Answer 1

The correct option is D (i) and (ii)

As we know, the sum of the interior angles of a triangle is ${180}^{\circ }$

i) According to the question,
${70}^{\circ }+{55}^{\circ }+{55}^{\circ }={180}^{\circ }$


ii) According to the question,
${70}^{\circ }+{70}^{\circ }+{40}^{\circ }={180}^{\circ }$

(iii) Not possible, because two angles must be equal in an isosceles triangle.

So (i) and (ii) can be possible.