Question

1. in △efg shown, fg has been extended through point g to point h. which of the following equations shows a relationship that is always true? (1) ( mangle3=mangle1 + mangle4 ) (2) ( mangle3=mangle1 + mangle2 ) (3) ( mangle2=mangle1 + mangle4 ) (4) ( mangle2=mangle3 + mangle4 )

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
In \(\triangle EFG\), \(\angle2\) is an exterior angle. The two non - adjacent interior angles are \(\angle1\) and \(\angle4\).
So, \(m\angle2=m\angle1 + m\angle4\)

Answer:

\((3)\) \(m\angle2=m\angle1 + m\angle4\)