Use the given angle to construct a new angle equal to [math]∠A + ∠A[/math].
Constructions can be created in more than one way. The steps in this applet show a different way to create the new angle than the steps provided below from the Guided Practice. [list=1] [*]Copy [math]∠A[/math] and label the vertex of the copied angle [math]G[/math]. [*]Put the sharp point of the compass on vertex [math]A[/math] of the original angle. Set the compass to any width that will cross both sides of the original angle. [*]Draw an arc across both sides of [math]∠A[/math]. Label where the arc intersects the angle as points [math]B[/math] and [math]C[/math]. [*]Without changing the compass setting, put the sharp point of the compass on [math]G[/math]. Draw a large arc that intersects one side of your newly constructed angle. Label the point of intersection [math]H[/math]. [*]Put the sharp point of the compass on [math]C[/math] of the original angle and set the width of the compass so it touches [math]B[/math]. [*]Without changing the compass setting, put the sharp point of the compass on point [math]H[/math] and make an arc that intersects the arc created in step 4. Label the point of intersection as [math]J[/math]. [*]Draw a ray from point [math]G[/math] to point [math]J[/math]. Do not erase any of your markings. [math]∠G = ∠A + ∠ A[/math] [/list]