Question

Find the value of A in the parallelogram.

Answer 1

a = 20

Explanation:

The opposite angles in a parellelogram are congruent.

⇒ 5a - 4 = 2a + 56

⇒ 5a - 2a = 56 + 4

⇒ 3a = 60

⇒
`a = (60)/(3)`

⇒ a = 20

Answer 2

a = 20

Explanation:

I apologize for my bad drawing (I can't draw well with a computer mouse), but opposite angles of a parallelogram are congruent. As seen in the picture, we can draw a line through and create two pairs of alternate interior angles.

One theorem in geometry states: when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

That means angle x + y = angle y + x which creates congruent angles. I drew it for the other two angles instead of those with the a's to not crowd the drawing.

Our newfound knowledge tells us that 5a - 4 = 2a + 56. With simple algebra, 3a= 60. We divide 3 from both sides and get a = 20