Given: <2 and <4 are vertical angles. Prove: <2 ~= <4

Statements Reasons

Assemble the proof by dragging tiles to
the Statements and Reasons columns

The proof of   are vertical angles is explained below.

Given, are vertical angles as shown in fig.

We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.

We have to prove that angle 2 and angle 4 congruent.

Given makes linear pair so,  

..........(1)

Again makes linear pair so,

.......(2)

From (1) and (2) we get,

Subtracting 180 from both the sides we get,

Or,

Hence angle 2 and angle 4 are congruent.

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Statement 1: and are vertical angles

Reason 1: Given

We basically just restate the given information word for word. This is true of any two column proof.

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Statement 2:  

Reason 2: and are a linear pair

The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.

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Statement 3:

Reason 3: and are a linear pair

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Statement 4:

Reason 4: Substitution

Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same

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Statement 5:

Reason 5: Subtraction property of equality

We subtracted the quantity from both sides (they go away)

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Statement 6:

Reason 6: Definition of congruence

If two items are congruent, then they have the same measure. In other words, they are the same.

85

Step-by-step explanation:

2x + 29 + x - 23 = 180

solve for x = 28

b = 2 * 28 + 29 = 85