Quadrilateral Hierarchy Math Example 4

Solution

1. 1
   Step 1: In a parallelogram, consecutive angles are supplementary: $\angle A + \angle B = 180°$. So $(3x+15) + (5x-5) = 180$.
2. 2
   Step 2: $8x + 10 = 180$, so $8x = 170$, giving $x = 21.25$.
3. 3
   Step 3: $\angle A = 3(21.25) + 15 = 63.75 + 15 = 78.75°$. $\angle B = 5(21.25) - 5 = 106.25 - 5 = 101.25°$.
4. 4
   Step 4: In a parallelogram, opposite angles are equal: $\angle C = \angle A = 78.75°$ and $\angle D = \angle B = 101.25°$. Check: $78.75 + 101.25 + 78.75 + 101.25 = 360°$. ✓