Question

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

Answer 1

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

Step-by-step 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