Question

A diagonal of parallelogram GHIJ forms angles with measures as shown
What is the measure of a. 40°
b. 79°
c. 101°
X d. 61°

Answer 1

<GIH:-

• 180-(79+40)
• 180-119
• 61

Now

• <IGJ=61°
• <GJI=79°

So

• <GIH=180-(79+61)=180-140=40°

Option A

Answer 2

In this case, we have a parallelogram:

  --> that means all the corresponding sides are parallel

         GJ -- parallel to -- HI

         GH -- parallel to -- JI

That means we can implement the alternate angle theorem

• Def of Alternate Angle Theorem: that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent

      * look at the diagram that I uploaded. The angles in there serve to

        show what angles are congruent

In this case, parallel lines GH and JI are cut by a transversal, GI, and thus we can implement the alternate angle theorem

   --> ∠GIJ = 40 degrees

Hope that helps!