Paper rectangle ABCD is folded in such a way that the fold passes through point B, and so A coincides with point H where H ∈ CD. BK is the folding line where K ∈ AD. m∠BKD = 120°. If BK = 28 cm, find BC.

The answer is BC = 38.22 cm.

Step-by-step explanation:

We have, ∠BKD = 120° ,BK = 28 cm, Draw a perpendicular from point K on BC let it intersect at point M.  In right angled ΔBMK, ∠BKM=30° and BK = 28 cm

sin30° = perpendicular/hypotenuse

1/2 = BM/BK

1/2 = BM/28

BM= 14 cm

Now , In right angled ΔBMK ,

cos30° = base/hypotenuse

√3/2 = MK/28

MK = 14√3 = 24.22 cm

KMCD is a square  MK = MC = 24.22 cm

also, BC = BM + MC , putting values of BM & MC we get :

BC = 14 cm + 24.22 cm

BC = 38.22 cm.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

24

step-by-step explanation:

you just have to add the 15 + 9 to get 24

you do this bc you want to find the total of the whole line and those two numbers make up the line