Exterior Angle Theorem

Exterior Angle Theorem For a triangle

• The exterior angle d equals the angles b plus c. (d = b + c)
• The exterior angle d is greater than angle b and angle c. (d^o > b^o, d^o > c^o)

Proof

d = b + c :

a + b + c = 180° (Because the interior angles of a triangle add to 180°)

a + d = 180°   (Angles a and d make a straight angle, which is 180°)

So

a + d = a + b + c

d = b + c

(d^o > b^o, d^o > c^o) :

Because d = b + c, where b and c are positive (in triangle) so we can say

d^o > b^o  

d^o > c^o

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Acute Angles

Obtuse Angles

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Supplementary Angles

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