Question

The angles of a triangle are in the ratio 2 : 5 : 2. What kind of triangle will it be?

A) Right angled, Isosceles
B) Obtuse angled, Isosceles
C) Obtuse angled, Scalene
D) Acute angled, may be isosceles or scalene

(please answer with steps...thnk you so much!)

Answer 1

$Given \: the \:angles \:of \:a\: triangle \: are \\in \:the \:ratio \: 2 : 5 : 2$

$Sum \: of \: the \:ratio = 2 + 5 + 2 = 9$

$9 \:parts = 180\degree \\ \blue {( Angle \:sum \: property )}$

$\implies 1 \: part = \frac{180}{9} = 20$

$First \:angle = 2 \:parts = 2\times 20 = 40\degree$

$Second\:angle = 5 \:parts = 5\times 20 = 100\degree$

$Third \:angle = 2 \:parts = 2\times 20 = 40\degree$

$40\degree, \:100\degree \:and \:40\degree \:are \: three \:angles \:of \: given \\triangle .$

$\therefore It \:is \: Obtuse \:angled ,\: isosceles \: triangle$

$Option \: \pink { ( B ) } \: is \: correct .$

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