Transversal Angles Math Example 2

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Example 2

medium
Two parallel lines are cut by a transversal. Co-interior angles (same-side interior angles) are 3x+10°3x + 10° and 5x−30°5x - 30°. Find xx and each angle.

Solution

  1. 1
    Step 1: Co-interior (same-side interior) angles between parallel lines are supplementary: they sum to 180°180°.
  2. 2
    Step 2: Set up the equation: (3x+10)+(5x−30)=180(3x + 10) + (5x - 30) = 180.
  3. 3
    Step 3: Simplify: 8x−20=1808x - 20 = 180, so 8x=2008x = 200, giving x=25x = 25.
  4. 4
    Step 4: First angle =3(25)+10=85°= 3(25) + 10 = 85°. Second angle =5(25)−30=95°= 5(25) - 30 = 95°. Check: 85+95=180°85 + 95 = 180°. ✓

Answer

x=25x = 25; angles are 85°85° and 95°95°.
Co-interior angles (also called same-side interior or consecutive interior angles) are supplementary when lines are parallel. This is different from alternate interior angles, which are equal. The word 'co-interior' hints at the same side — and angles on the same side of a transversal between parallel lines add to 180°.

About Transversal Angles

When a transversal (a line that crosses two parallel lines), it creates eight angles with four special relationships: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (same-side interior) angles are supplementary.

Learn more about Transversal Angles →

More Transversal Angles Examples

Example 1 easy

A transversal crosses two parallel lines. One of the angles formed is [formula]. Find the correspond

Example 3 easy

A transversal crosses two parallel lines. An alternate exterior angle is [formula]. What is the meas

Example 4 hard

Lines [formula] and [formula] are cut by a transversal. Corresponding angles are [formula] and [form

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