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Diano4ka-milaya [45]
3 years ago
5

Find the values of x and y for which this quadrilateral must be a parallelogram.

Mathematics
2 answers:
leonid [27]3 years ago
5 0
The answer is 17 I hope this helps
Liono4ka [1.6K]3 years ago
4 0

Answer:

x=7 and y=17

Step-by-step explanation:

Let's start by calling the center of the parallelogram O

In a parallelogram diagonals bisect meaning that  BO = OD and similarly CO=OA

BO=OD

4x-8=20 (Just subsituting values for BO an OD)

4x=28

x=7

CO=OA

2y-6=28 (Subsituting values for CO and OA)

2y=34

y=17

So...

x=7 and y=17

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Given: ABCD parallelogram BK ⊥ AD , AB = 6, AK = 3 Find: m∠A, m∠B, m∠C, m∠D
Troyanec [42]

Answer: Angle A = 60°, angle B = 120°, angle C = 60°, angle D = 120°

Step-by-step explanation: Please refer to the attached diagram for further details.

The question has given the parallelogram ABCD as having side AB measuring 6 units, side AK measuring 3 units and line BK has been drawn perpendicular to line AD. This means line AK forms a right angle at the point where it meets line AD. From the information provided and the figure derived from that, we have right angled triangle ABK with the right angle at point K, line AB equals 6 units and line AK equals 3 units.

Using angle A as the reference angle, line AK is the opposite (side facing the reference angle), line AB is the hypotenuse (line facing the right angle) and line AK is the adjacent (side that lies between the right angle and the reference angle).

Hence, using the trigonometric ratios,

Cos A = adjacent/hypotenuse

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Cos A = 0.5

Checking with the calculator, (that is second function of Cos 0.5)

A = 60

The opposite sides of a parallelogram are equal (that is line AD is parallel to line BC) and therefore opposite angles are equal (that is angle A is equal to angle C).

Similarly, angle B is equal to angle D. However, angles in a quadrilateral equals 360 degrees.

Therefore, angles in parallelogram ABCD is derived as;

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