Question

Please I just need help so badly asap Please

Answer 1

- It is a parallelogram

Explanation:

- The interior angle sum of a quadrilateral is 360°

Considering the four angles;

`{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( (3)/(2) x - 15) + ( (7)/(3) x - 12) = 360}} \\ \\ { \tt{(x + 2x + (3)/(2)x + (7)/(3)x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ (41)/(6) x - 9 = 360}} \\ \\ { \tt{ (41)/(6)x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}`

- Therefore, substitute in x and find the angles.

`{ \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( (3)/(2)x - 15) = \{( (3)/(2) * 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( (7)/(3)x - 12) = \{( (7)/(3) * 54) - 12 \} = 114 \degree }}`