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3 years ago

The measure of ∠1 = 188 172 94

Mathematics

1 answer:

yanalaym [24]3 years ago

4 0

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

There is a cyclic quadrilateral.

As we know that "Sum of opposite angles in a cyclic quadrilateral is supplementary.":

so, it becomes,

$86^\circ+\angle 1=180^\circ\\\\\angle 1=180^\circ-86^\circ\\\\\angle 1=94^\circ$

Hence, the measure of ∠1 = 94°

Therefore, Third option is correct.

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Step-by-step explanation:

the question to the problem is to write the values of the first term, common ratio, and expression for the recursive rule.

The first term :

In geometric sequence, the first term is given as $a_{1}$ .

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Now, the geometric sequence follows as 612, 661, ........

The common ratio (r) :

It is the ratio between two consecutive numbers in the sequence.

Therefore, to determine the common ratio, you just divide the number from the number preceding it in the sequence.

⇒ r = 661 divided by 612

⇒ r = 1.08

To find the recursive rule :

A geometric series is of the form a,ar,ar2,ar3,ar4,ar5........

Here, first term $a_{1} = a$ and other terms are obtained by multiplying by r.

Observe that each term is r times the previous term.
Hence to get nth term we multiply (n−1)th term by r .

The recursive rule is of the form $a_{n} = a^{n-1} \times r$

This is called recursive formula for geometric sequence.

We know that r = 1.08 and $a_{1}$ = 612.

To find the second term $a_{2}$ , use the recursive rule $a_{n} = a^{n-1} \times r$

⇒ $a_{2} = a^{2-1}\times r$

⇒ $a_{2} = a^{1}\times r$

⇒ $a_{2} = 612\times 1.08$

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