# FINDING UNKNOWN ANGLE MEASURES

We can find any unknown angle measure when two parallel lines are cut by a transversal, if we are given at least one other angle measure.

Example 1 :

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m2 when m7 = 120°. Solution :

Step 1 :

In the above diagram, m2 and m∠7 are alternate interior angles.

Step 2 :

When two parallel lines are cut bu a transversal, alternate interior angles are congruent.

So, we have

m2  =  m∠7

m2  =  120°

Example 2 :

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find mVWZ. Solution :

Step 1 :

In the above diagram, m∠VWZ and m∠YVW are same-side interior angles.

Step 2 :

When two parallel lines are cut by a transversal, same-side interior angles are supplementary.

So, we have

m∠VWZ + m∠YVW  =  180°

Step 3 :

From the diagram given above, we have m∠VWZ = 3x and m∠YVW = 6x. So, replace m∠VWZ by 3x and m∠YVW by 6x.

3x + 6x  =  180°

Combine like terms.

9x  =  180°

Divide both sides by 9.

9x/9  =  180°/9

Simplify.

x  =  20°

Step 4 :

Plug x = 20° in m∠VWZ = 3x.

m∠VWZ  =  3 · 20°

m∠VWZ  =  60°

Example 3 :

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠GDE. Solution :

Step 1 :

In the above diagram, m∠GDE and m∠ADE are angles on the straight line l.

So, we have

m∠GDE + m∠ADE  =  180° ----- (1)

Step 2 :

In the above diagram, m∠ADE and m∠BEF are corresponding angles and corresponding angles are always congruent.

So, we have

Step 3 :

In (1) replace m∠ADE by m∠BEF

(1) -----> m∠GDE + m∠BEF  =  180°

Step 4 :

From the diagram given above, we have m∠GDE = 4x and m∠BEF = 6x. So, replace m∠GDE by 4x and m∠BEF by 6x.

4x + 6x  =  180°

Combine like terms.

10x  =  180°

Divide both sides by 10.

10x/10  =  180°/10

Simplify.

x  =  18°

Step 5 :

Plug x = 18° in m∠GDE  =  4x

m∠GDE  =  4 · 18°

m∠GDE  =  72°

Example 4 :

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠3 when m∠6 = 65°. Solution :

Step 1 :

In the above diagram, m∠3 and m∠6 are alternate interior angles.

Step 2 :

When two parallel lines are cut bu a transversal, alternate interior angles are congruent.

So, we have

m∠3  =  m∠6

m2  =  65° Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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