Question

If the ratio of angles in a triangle is 1:2:3 then find the value of the greatest angle and the smallest angle in the triangle.

• A. Greatest angle is 90${}^{\circ }$
• B. Greatest angle is 180${}^{\circ }$
• C. Smallest angle is 60${}^{\circ }$
• D. Smallest angle is 30${}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A

Greatest angle is 90${}^{\circ }$

D

Smallest angle is 30${}^{\circ }$

Given the ratio of angles in a triangle is 1:2:3

$\therefore$ Let the angles be $x$, 2$x$, 3$x$.

$\because$ Sum of angles in a triangle = 180${}^{\circ }$

$\Rightarrow$ $x$ + 2$x$ + 3$x$ = 180${}^{\circ }$

$\Rightarrow$ 6$x$ = 180${}^{\circ }$

$\Rightarrow$ $x$ = 30${}^{\circ }$

Now the greatest angle = 3$x$

= 3 $\times$ 30${}^{\circ }$

= 90${}^{\circ }$

and smallest angle = $x$

= 30${}^{\circ }$