Question

If one angle of a triangle is equal to the sum of other two.Show that the triangle is a right triangle

Answer 1

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Answer 2

$let \: the \: triangle \: whose \: angles \: are \: a \: b \: and \: c \\ \\ atq \\ a = b + c - - - - - - i \\ \\ by \: angle \: sum \: property \: of \: triangle \\ a + b + c = 180 - - - - - - - ii \\ from \: eq \: (i) \\ \\ a + b + c = a + a = 180 \: \: \: \: \: \: \: \: \: (a = b + c) \\ \\ now \: \: \\ 2a = 180 \\ a = 90 \\ \\ therefore \: an \: angle \: of \: triangle \: abc \: is \: 90 \\ \\ therefore \: given \: triangle \: is \: a \: right \: angled \: triangle \\ \times \times - - - - - - - - - - \times \times \times henc \: roved$
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