Question

Use rhombus ABCD and the given information to find each value.​

Answer 1

Answer: (c) 31 (d) 30 (e) 41 (f) 10

Explanation:

NOTES about angles of a rhombus:

1. diagonals are angle bisectors (cut the angle into 2 equal parts)
2. diagonals are perpendicular to each other (90°)
3. 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