Answer:
see explanation
Explanation:
the diagonals of a rhombus are perpendicular to each other, then
∠ 1 = 90°
AB and CD are parallel ( opposite sides of a rhombus are parallel )
∠ 2 and 51° are alternate angles and are congruent , then
∠ 2 = 51°
the diagonals bisect the angles , then
∠ 3 = ∠ 2 = 51°
the sum of the 3 angles , in the triangle with ∠ 4 sum to 180°
∠ 1 + ∠ 3 + ∠ 4 = 180°
90° + 51° + ∠ 4 = 180°
141° + ∠ 4 = 180° ( subtract 141° from both sides )
∠ 4 = 39°
then
∠ 1 = 90° , ∠ 2 = 51° , ∠ 3 = 51° , ∠ 4 = 39°