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Sunny_sXe [5.5K]
1 year ago
11

The sum of two consecutive even integers divided by four is 189.5

Mathematics
1 answer:
Andre45 [30]1 year ago
6 0
The sum of two consecutive even integers is a+(a+2) and divided by four is
(a+(a+2))/4 = 189.5
(2a+2)/4 = 189.5
2a+2 = 189.5 * 4
2a+2 = 758
2a = 758 - 2
2a = 756
a = 756/2 = 378
first number is a = 378
second number is a+2 = 378+2 = 380
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one angle of a linear pair is 10 more than two thirds the other angle. find the measure if both angles
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Answer:

One Angle = 110°

Other Angle = 70°

Step-by-step explanation:

A linear pair means that two angles are in a straight line (or, a straight angle).

A straight line is 180 degrees.

THey are supplementary.

We can say one angle is "a" and another one is "b".

<em>One angle is 10 MORE THAN 2/3rds of the other, we can write:</em>

<em>a=\frac{2}{3}b+10</em>

<em />

<em>Also, since they are supplementary (add up to 180), we can write:</em>

<em>a + b = 180</em>

<em />

We can now substitute 1st equation in this one and find b:

a+b=180\\(\frac{2}{3}b+10)+b=180\\\frac{2}{3}b+b=180-10\\\frac{5}{3}b=170\\b=\frac{170}{\frac{5}{3}}\\b=170*\frac{3}{5}\\b=110

Since a + b = 180, we can write:

a + 110 = 180

so,

a = 180 - 110

a = 70

Thus,

One Angle = 110°

Other Angle = 70°

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