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

psiha47h

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.
$\therefore x+x+2x={180}^{\circ }\phantom{\rule{0ex}{0ex}}⇒4x={180}^{\circ }\phantom{\rule{0ex}{0ex}}⇒x={45}^{\circ }$
∴ The angles are .
∴ The largest angle is ${90}^{\circ }$.

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