Question

Need help please ! parallelogram

Answer 1

11). m∠W = 70°

12). m∠M = 95°

13). m∠Q = 135°

14). m∠Q = 55°

15). m∠X = 110°

Explanation:

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

(24x - 2) + (36x + 2) = 180°

60x = 180°

x =
`(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 =
`(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°