Question

The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle?

• A. 90${}^{\circ }$
• B. 135${}^{\circ }$
• C. 45${}^{\circ }$
• D. 150${}^{\circ }$

Answer 1

The correct option is A 90${}^{\circ }$

From Legendre's theorem, we know that "The sum of all the angles of a triangle is constant and equal to two right angles".
Let the angles be x, x and 2x.
$\therefore$ x + x + 2x = 180${}^{\circ }$
$\Rightarrow$ 4x = 180${}^{\circ }$
$\Rightarrow$ x = 45${}^{\circ }$.

$\therefore$ The angles are 45${}^{\circ },$ 45${}^{\circ }$ and 90${}^{\circ }$.
$\therefore$ The largest angle is 90${}^{\circ }$.