Angle Relationships Math Example 3

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

Example 3

easy
Angle AA and angle BB are complementary. If ∠A=4x+3°\angle A = 4x + 3° and ∠B=2x+9°\angle B = 2x + 9°, find both angles.

Solution

  1. 1
    Step 1: Complementary angles sum to 90°90°: (4x+3)+(2x+9)=90(4x + 3) + (2x + 9) = 90.
  2. 2
    Step 2: 6x+12=906x + 12 = 90, so 6x=786x = 78, giving x=13x = 13.
  3. 3
    Step 3: ∠A=4(13)+3=55°\angle A = 4(13) + 3 = 55° and ∠B=2(13)+9=35°\angle B = 2(13) + 9 = 35°. Check: 55+35=90°55 + 35 = 90°. ✓

Answer

∠A=55°\angle A = 55°, ∠B=35°\angle B = 35°.
Complementary angles sum to 90°. Setting up the equation with the algebraic expressions and solving for xx is the standard approach. Always verify by substituting back and confirming the angles sum to 90°.

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 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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