Question

In $\Delta ABC,2\angle A=3\angle B,5\angle B=2\angle C$. Then the triangle is

• A. Isosceles
• B. Right-angled
• C. Equilateral
• D. Right-angled and isosceles

Answer 1

The correct option is B Right-angled

$2\angle A=3\angle B$
$and5\angle B=2\angle C$
$\angle A+\angle B+\angle C={180}^o$
$\therefore \frac{3}{2}\angle B+\angle B+\frac{5}{2}\angle B={180}^o$
$5\angle B=180or\angle B={36}^o$
$\therefore \angle A=\frac{3}{2}\times 30={54}^o$
$and\angle C=\frac{5}{2}\times 36={90}^o$
Therefore, the triangle is right-angled.