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Prove that the sum of the three angle of triangle is two right angle in a right angle triangle an acute is one fourth the other,find the acute angle.



Let ABC is a triangle
To prove: to prove all the sum of side is 180°
construction: draw a line DE through the point A such that DE is parallel to BC
DE is parallel to BC and AC & BA are transversal
 and ∠EAC =∠ACB
we know
∠DAB +∠BAC+∠EAC=180° [straight line]
we can also write that
∠ABC+∠BAC+∠ACB= 180°
                                      Hence proved
which is equl to 2 right angle 90° + 90° = 180°
In a right angled triangle
one angle is x
second angle is  \frac{1}{4} x
third angle 90°
90°+x +   \frac{1}{4} x =180°
x + \frac{x}{4} + 90°= 180°
x = 75°
the  second angle (acute angle)=  \frac{75}{4} =18.5

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