Question

I was absent from school and I have a homework assignment about justifying statements for geometry

Answer 1

1) If point M is the midpoint of the line segment AB, then we can state that

`\overline{AM}\cong\mathbf{\overline{MB}}`

Because of the definition that states the Midpoint is the point the divides a line segment into two congruent line segments.

2) Notice that we have a pair of angles adjacent angles. In this case, we have a Linear pair.

So, if :

`if\: m\angle1\: and\: m\angle2\: form\: a\: \mathbf{Linear\: Pair}`

then m∠1 + m∠2 = 180º because their sum makes up a Straight Angle

3)

If we have m∠1 =5x +50 and m∠2=60x then we can write out:

5x+50 + 60x = 180º

65x +50 = 180

65x +50-50 = 180-50

65x = 130

x= 130/65

x = 2

m∠1 =5x +50 = 5(2) +50 = 60

m∠2=60x = 60 (2) = 120

120º+60º = 180º True