**Finding unknown angle measures worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on finding angle measures when two parallel lines are cut by a transversal.

1. In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠2 when m∠7 = 120°.

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

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

4. In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠7 when m∠6 = 65°.

**Problem 1 :**

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠2 when m∠7 = 120°.

**Solution : **

**Step 1 : **

In the above diagram, m∠2 and m∠7 are alternate interior angles.

**Step 2 : **

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

So, we have

m∠2 = m∠7

m∠2 = 120°

**Problem 2 :**

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

**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°

**Problem 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 l₁.

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

m∠ADE = m∠BEF

**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°

**Problem 4 :**

In the diagram given below, the lines l₁ and l₂ are parallel and the line T is transversal. Find m∠7 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 by a transversal, alternate interior angles are congruent.

So, we have

m∠3 = m∠6

m∠2 = 65°

After having gone through the stuff given above, we hope that the students would have understood "Finding unknown angle measures worksheet".

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