12. If one angle of a triangle is equal to the sum of the
other two, show that the triangle is a right triangle.
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Step-by-step explanation:
let the first angle of the triangle be x
let the second angle of the triangle be y
and the third angle be x+y (because sum of two angle
is equal to the third angle)
then, according to angle sum property of triangle,
x + y + ( x+y) = 180°
2x + 2y = 180°
2 (x + y) = 180° [ taking 2 common]
x + y = 180/2
x + y = 90
Therefore, the third angle which is (x +y) is 90°, the triangle is a right angle triangle.
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