Question

Need help please ! parallelogram

Answer 1

Answer:

11). m∠W = 70°

12). m∠M = 95°

13). m∠Q = 135°

14). m∠Q = 55°

15). m∠X = 110°

Step-by-step explanation:

11). m∠W + m∠X = 180° [Consecutive interior angles]

    (24x - 2) + (36x + 2) = 180°

     60x = 180°

     x = $\frac{180}{60}$

     x = 3

     Therefore, m∠W = (24x - 2)°

     m∠W = (24×3 - 2)

               = 72 - 2

               = 70°

     Since opposite angles of a parallelogram are equal in measure.

     m∠Y = m∠W = 70°

12). m∠J + m∠K = 180° [Consecutive interior angles]

     (6x + 19) + (8x + 7) = 180°

     14x + 26 = 180

     14x = 180 - 26

     14x = 154

     x = $\frac{154}{14}$

     x = 11

     m∠K = (8x + 7)

     m∠K = 8×11 + 7

     m∠K = 95°

     Since m∠M = m∠K

     Therefore, m∠M = 95°

13). m∠Q = m∠S [Opposite angles of a parallelogram]

      x + 135 = 2x + 135

      2x - x = 0

      x = 0

      Therefore, m∠Q = 135°

14). m∠Q = m∠S [Opposite angles of a parallelogram]

      14x - 1 = 13x + 3

      14x - 13x = 3 + 1

      x = 4

      m∠Q = (13x + 3)

                = 13×4 + 3

                = 52 + 3

      m∠Q = 55°

15). m∠Z = m∠X

     (19x - 4) = (17x + 8)

      19x - 17x = 12

      2x = 12

      x = 6

      m∠X = (17x + 8)°

      m∠X = 17×6 + 8

      m∠X = 110°