Angle Relationships Math Example 2

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Example 2

medium
Two lines intersect forming four angles. One angle is 124°124°. Find all four angles.

Solution

  1. 1
    Step 1: Two intersecting lines form two pairs of vertical angles. The angle opposite the 124°124° angle is also 124°124° (vertical angles are equal).
  2. 2
    Step 2: The other two angles are supplementary to 124°124°: 180°−124°=56°180° - 124° = 56°.
  3. 3
    Step 3: These two angles are also vertical to each other, so both equal 56°56°.
  4. 4
    Step 4: The four angles are: 124°124°, 56°56°, 124°124°, 56°56°.

Answer

The four angles are 124°124°, 56°56°, 124°124°, and 56°56°.
When two lines intersect, they form two pairs of vertical (opposite) angles. Vertical angles are always equal. Adjacent angles in the intersection are supplementary (they form a straight line). These two properties together determine all four angles once any one is known.

About Angle Relationships

Fundamental relationships between pairs of angles: supplementary angles sum to 180°180°, complementary angles sum to 90°90°, vertical angles are equal, and adjacent angles share a common ray.

Learn more about Angle Relationships →

More Angle Relationships Examples

Example 1 easy

Two angles are supplementary. One angle measures [formula]. Find the other angle.

Example 3 easy

Angle [formula] and angle [formula] are complementary. If [formula] and [formula], find both angles.

Example 4 hard

Three angles share a common vertex and together form a straight line. The angles are in the ratio [f

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