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mel-nik [20]
3 years ago
6

5. Prove that opposite angles of a cyclic quadrilateral are supplementary.

Mathematics
1 answer:
Temka [501]3 years ago
3 0

Answer:

See attached for the cyclic quadrilateral

To prove: <BAD + <BCD =180°

Construction: Join B and D to the centre O of circle ABCD

Proof  

With the lettering of the attached drawing,

                         <BOD = 2y    (angle at centre is 2 X angle at circumference)

            Reflex <BOD   = 2x     (angle at centre is 2 X angle at circumference)

                    ∴ 2x + 2y = 360°    (angle at point)

                       ∴ x + y   = 180°                    

       ∴ <BAD + <BCD   = 180°            

Step-by-step explanation:

The vertices of a cyclic quadrilateral lie on the circumference of the circle and the opposite angles of a cyclic quadrilateral lie in opposite segment of a circle.

The question is to prove that the opposite angles of a cyclic quadrilateral are supplementary that is 180°. Another way of stating this theory is 'Angles in opposite segments are supplementary'.

Note that the sum of supplementary angles is 180°.

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Answer:

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Step-by-step explanation:

-3a + 7 +5a

<em>subtract the negative 3 from the 5</em>

2a + 7

4 0
3 years ago
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
The lines whose equations are 2x + y = 3z and x + y = 6z intersect at which point?
Tema [17]
2x + y - (x + y) = 3z - 6z 
--------------------------------------------------------
<span>x = -3z </span>
------------------------------------------

<span>(-3z, 9z) </span>
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3 0
3 years ago
a rectangle is made by joining two squares adjacent to each other as shown below. if one squared has an area of 144 squared cent
liberstina [14]

Answer:

Hello! After reading your question I have deduced that the correct answer is 288² cm.

Step-by-step explanation:

The way I came to this conclusion was as follows:

Firstly:

If said rectangle is two squares put side by side (adjacent), then a valid assumption is that both squares are the same size.

This is because all four sides of a square have to be equal.

Thus if the two squares are joined together on one side, then all the other sides of both the squares will be the same length.

Thus both of the squares are going to be the same size, so they will have the same area.

Secondly:

If the area of one square is 144² cm then the area of the other square should also be 144² cm.

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I hope this helped!

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2 years ago
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Novosadov [1.4K]

Answer:

-4.67

Step-by-step explanation:

first find f^-1(x)

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Therefore f^-1(x)=x-2/3

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8 0
2 years ago
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