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Gnoma [55]
3 years ago
9

Given:quadrillateral ABCD inscribed in a circle

Mathematics
1 answer:
son4ous [18]3 years ago
5 0

Answer:

Step-by-step explanation:

Given: quadrilateral ABCD inscribed in a circle

To Prove:

1. ∠A and ∠C are supplementary.

2. ∠B and ∠D are supplementary.

Construction : Join AC and BD.

Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,

∠1=∠2-----(1)

∠3=∠4-----(2)

∠5=∠6-------(3)

∠7=∠8------(4)

Also, sum of angles of quadrilateral is 360°.

⇒∠A+∠B+∠C+∠D=360°

→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4

→→→2∠1+2∠4+2∠6+2∠8=360°

→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,

→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)

As, ∠A+∠B+∠C+∠D=360°

∠A+∠C+180°=360°

∠A+∠C=360°-180°------Using A

∠A+∠C=180°

Hence proved.

credit: someone else

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Step-by-step explanation:

Given: Allan drew a polygon with 4 sides and 4 angles with two properties:-

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Therefore, the figure drawn by Alan is a rhombus.


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<span> (x + 3) • (x - 12)
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The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
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Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -36 = -36</span> 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is  <span> -9 </span>.

<span><span>     -36   +   1   =   -35</span><span>     -18   +   2   =   -16</span><span>     -12   +   3   =   -9   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3 
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Step-4 : Add up the first 2 terms, pulling out like factors :
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Step-5 : Add up the four terms of step 4 :
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      x^2-12x+45
       ___ ________________________
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      - (x^3+x^2)
       _________________________
            -12x^2+33x+45
          - (-12x^2-12x)
          ______________
            45x+45
         -(45x+45)
___________
0


Since that works, it's either B or D. We just have to figure out when
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8 0
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