Answer:
∠C = 48°
Explanation:
The opposite angles at B and D are congruent, thus
5x - 147 = 2x ( subtract 2x from both sides )
3x - 147 = 0 ( add 147 to both sides )
3x = 147 ( divide both sides by 3 )
x = 49
∠B = 2x = 2 × 49 = 98°
∠D = 5x - 147 = (5 × 49) - 147 = 245 - 147 = 98°
The 4 interior angles of a kite sum to 360°
Subtract the sum of the known angles from 360 for ∠C
∠C = 360° - (116 + 98 + 98)° = 360 - 312 = 48°
The 4 interior angles of the kite are 116°, 98°, 98°, 48°
The smallest angle is ∠C = 48°