Question

if a:b =2:3 and anglea and angle b are in linear pair then m angle b =í​

Answer 1

Answer:

if a:b =2:3 and anglea and angle b are in linear pair then m angle b =í

Step-by-step explanation:

Answer

Given integers are 81 and 237 such that 81<237.

Applying division lemma to 81 and 237, we get

237=81×2+75

Since the remainder 75

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=0. So, consider the divisor 81 and the remainder 75 arndapply division lemma to get

81=75×1+6

We consider the new divisor 75 and the new remainder 6 and apply division lemma to get

75=6×12+3

We consider the new divisor 6 and the new remainder 3 and apply division lemma to get

6=3×2+0

The remainder at this stage is zero. So, the divisor at this stage or the remainder at the earlier stage i.e. 3 is the HCF of 81 and 237.

To represent the HCF as a linear combination of the given two numbers, we start from the last but one step and successively eliminate the previous remainder as follows:

From (iii), we have

3=75−6×12

⇒3=75−(81−75×1)×12

⇒3=75−12×81+12×75

⇒3=13×75−12×81

⇒3=13×(237−81×2)−12×81

⇒3=13×237−26×81−12×81

⇒3=13×237−38×81

⇒3=237x+81y, where x=13 and y=−38.

Now the HCF (say d) of two positive integers a and b can be expressed as a linear combination of a and b i.e., d=xa+yb for some integers x and y.

Also, this representation is not unique. Because,

d=xa+yb

⇒d=xa+yb+ab−ab

⇒d=(x+b)a+(y−a)b

In the above example, we had

3=13×237−38×81

⇒3=13×237−38×81+237×81−237×81

⇒3=(13×237+237×81)+(−38×81−237×81)

⇒3=(13+81)×237+(−38−237)×81

⇒3=94×237−275×81

⇒3=94×237+(−275)×81

Answer 2

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As with all angle problems, you have to be able to identify the relationship between the given angles and mst know the definition of different angle pairs. Your problem stated that the given angles are linear pairs. By definition , linear pairs are adjacent angles that form a straight line and are supplementary, meaning the angles add up to 180 degrees. Now you have an equation you can use to solve for x.

m<A + m<B = 180

2x + 8 + 3x + 2 = 180 Now solve for x

5x + 10 = 180. Combine like terms

- 10 - 10 subtract 10 from both sides

5x = 180 divide both side by 5

x = 34

Now that you know x, you can also find m<A and m<B and should check that these angles add up to 180 degrees.