The exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle
([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8) then m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .
What is meant by Exterior Angle Inequality Theorem?
According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle ([tex]\angle[/tex] 2) is larger than either remote interior angle ([tex]\angle[/tex] 6 and [tex]\angle[/tex] 8).
Similarly, the exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle ([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8).
Therefore, m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .
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