Angle Relationships Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Three angles share a common vertex and together form a straight line. The angles are in the ratio 1:2:31:2:3. Find each angle.

Solution

  1. 1
    Step 1: Angles on a straight line sum to 180°180°. Let the angles be kk, 2k2k, and 3k3k.
  2. 2
    Step 2: k+2k+3k=180°k + 2k + 3k = 180°, so 6k=180°6k = 180°, giving k=30°k = 30°.
  3. 3
    Step 3: The three angles are 30°30°, 60°60°, and 90°90°.

Answer

The three angles are 30°30°, 60°60°, and 90°90°.
Angles that together form a straight line are called supplementary (for two angles) or, more generally, they sum to 180°. Using the ratio 1:2:31:2:3 means the parts are in proportion, so set each part as a multiple of kk and solve. The result (30°30°-60°60°-90°90°) happens to match the angles of a special right triangle.

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 2 medium

Two lines intersect forming four angles. One angle is [formula]. Find all four angles.

Example 3 easy

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

← All Angle Relationships Examples Angle Relationships Concept