Unknown Angles – Parallel Lines

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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. This is because for two parallel lines and a transversal,  

• corresponding angles are equal
• alternate angles are equal
• the same side interior angles are supplementary (sums to 180⁰).

Example 1.

Corresponding angles are equal.

Let us call the missing angle x. Then, x = 53⁰.

Example 2.

Alternate angles are equal

Let us call the missing angle x. Then, x = 125⁰

Example 3.

The same side interior angles are supplementary (sums to 180⁰).

Let us call the missing angle x, then x = 180⁰ – 100⁰ = 80⁰.

Example 4.

Solve for x.

Corresponding angles are equal.

Then, 23x – 5 = 21x + 5

        – 21x – 21x

—————————-

           2x – 5 = 5

  + 5  + 5

—————————-

2x = 10

x = 5

Example 5.

Solve for x.

Alternate angles are equal

Then, 

8x – 4 = 60

    + 4    +4

————–

    8x = 64

      x  = 8 

Example 6.

Solve for x, then find the value of each angle.

The same side interior angles are supplementary (sums to 180⁰).

Then,

(x + 109) + (x + 89) = 180

2x +198 = 180

2x = 180 – 198 

x = – 9 

Therefore, x + 109 = – 9 +189 = 100 and, x + 89 = – 9 + 89 = 80. 

Solve the following problems.

Find the indicated angle in each problem.

Solve for x, then find the value of the indicated angle.