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den301095 [7]
3 years ago
15

Please can some explain how to identify angles that on the same segment? ​

Mathematics
1 answer:
sp2606 [1]3 years ago
8 0

Step-by-step explanation:

Angles in the same segment. The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Picture 1  a° = a°  they are the same

Picture 2  p= 52°  q= 40° Angles in the same segment are equal. if they ask you to calculate you just show both angles p= 52 and q=40.

Picture 3 + 4  Let the obtuse angle MOQ = 2x.  

Using the circle theorem, the angle at the centre is twice   the angle at the circumference.

Therefore picture 4 tells us and proves;

Angle MNQ = x and angle MPQ = x.

Picture 5

A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every corner of the quadrilateral must touch the circumference of the circle.

The second shape is not a cyclic quadrilateral. One corner does not touch the circumference.

Picture 6

The opposite angles in a cyclic quadrilateral add up to 180°.

a + c = 180°

b + d = 180°

Picture 7

Example

Calculate the angles a and b.

The opposite angles in a cyclic quadrilateral add up to 180°.

This is a picture that couldn't be added but has a quadrilateral occupying half the triangle consisting of 3 arcs the middle one was 140 and proved part of one triangle. The x (a) missing angle showed below a = 180-60 = 120 °

So hopefully this will help you remember the format here for quadrilateral shapes within a circle.

b = 180 - 140 = 40°

a = 180 - 60 = 120°

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Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.
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Answer:

<h3>The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

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(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

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a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

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Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

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