In parallelogram abcd, ab=14, bc=20, m (angle) b=54. Find to the nearest tenth the length of diagonal bd, and find measure angle dbc to the nearest degree.

It is is a parallelogram, hence we have to face sides equal in length and the opposite angles are also the same. From the given above we have:

ab=14 and its opposite side cd=14

bc=20 and its opposite side da=20

Solving for the diagonal measurement bd, we have consecutive angles are equal to 180°

∠A+∠B=180°

∠A=180°-54°

∠A=126°, ∠B=54°,∠C=126° and ∠D=54°

bd²=ab²+da²-2 (ab) (da) cos126°

bd²=14²+20²-2*14*20cos126°

bd=30.42 unit

Solving for the angle dbc, we have

cos dbc=bc²+bd²-cd²/a*bc*bd

cos dbc=20²+30.42²-14²/2*20*30.42

dbc=21.76°