Answer: (c) 31 (d) 30 (e) 41 (f) 10
Step-by-step explanation:
NOTES about angles of a rhombus:
- diagonals are angle bisectors (cut the angle into 2 equal parts)
- diagonals are perpendicular to each other (90°)
- two adjacent triangles of a rhombus form an isosceles triangle
(c) Given: ∠CBD = 59°
Per rule 2 → ∠BEC = 90°
Triangle Sum Theorem: sum of the angles of a triangle = 180°
∠CBD + ∠BEC + ∠BCE = 180°
59° + 90° + ∠BCE = 180°
149° + ∠BCE = 180°
∠BCE = 31°
(d) Given: ∠BCD = 120°
Per rule 3 → ∠CBD = ∠CDB
Triangle Sum Theorem: sum of the angles of a triangle = 180°
∠CBD + ∠CDB + ∠BCD = 180°
2∠CBD + 120° = 180°
2∠CBD = 60°
∠CBD = 30°
(e) Given: ∠AED = 2x+8
Per rule 2 → ∠AED = 90°
2x+8 = 90
2x = 82
x = 41
(f) Given: ∠BCE = 3x + 3 and ∠ECD = 5x - 17
Per rule 1 → ∠BCE = ∠ECD
3x + 3 = 5x- 17
3 = 2x - 17
20 = 2x
10 = x
