Kole Meyers

2023-03-11

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

$A){90}^{\circ}\phantom{\rule{0ex}{0ex}}B){135}^{\circ}\phantom{\rule{0ex}{0ex}}C){45}^{\circ}\phantom{\rule{0ex}{0ex}}D){150}^{\circ}$

$A){90}^{\circ}\phantom{\rule{0ex}{0ex}}B){135}^{\circ}\phantom{\rule{0ex}{0ex}}C){45}^{\circ}\phantom{\rule{0ex}{0ex}}D){150}^{\circ}$

psiha47h

Beginner2023-03-12Added 2 answers

The right response is A ${90}^{\circ}$

According to Legendre's theorem, "the total of all the angles of a triangle is fixed and equal to two right angles."

Let the angles be x, x and 2x.

$\therefore x+x+2x={180}^{\circ}\phantom{\rule{0ex}{0ex}}\Rightarrow 4x={180}^{\circ}\phantom{\rule{0ex}{0ex}}\Rightarrow x={45}^{\circ}$

∴ The angles are ${45}^{\circ},{45}^{\circ}\text{and}{90}^{\circ}$.

∴ The largest angle is ${90}^{\circ}$.

According to Legendre's theorem, "the total of all the angles of a triangle is fixed and equal to two right angles."

Let the angles be x, x and 2x.

$\therefore x+x+2x={180}^{\circ}\phantom{\rule{0ex}{0ex}}\Rightarrow 4x={180}^{\circ}\phantom{\rule{0ex}{0ex}}\Rightarrow x={45}^{\circ}$

∴ The angles are ${45}^{\circ},{45}^{\circ}\text{and}{90}^{\circ}$.

∴ The largest angle is ${90}^{\circ}$.