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VMariaS [17]
3 years ago
10

Find the value of x and the unknown angle in each problem

Mathematics
1 answer:
Gnom [1K]3 years ago
4 0
Hello!

Angle POQ and angle MON are vertical which means they are congruent

x - 28 = 149

Add 28 to both sides

x = 177

Angle NOQ and angle NOM are supplementary meaning they add to 180

NOQ + NOM = 180

Put in the known angle

NOQ + 149 = 180

Subtract 149 from both sides

NOQ = 31

The answers are x = 177 and angle NOQ = 31

Hope this helps!
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Given:

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Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.  

Let r be any rational number.

We have,

3r^2-2r+4

It can be written as

3(r\times r)-2r+4

Now,

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r^2=r\times r is rational by Property 3.

3r^2\text{ and }-2r are rational by Property 3.

3r^2+(-2r)+4 is rational by property 2.

So, 3r^2-2r+4 is rational.

Hence proved.

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