Question

Two angles are making a linear pair. If one of them is one third the other , find the angles

Answer 1

Answer:

The angle measures that make a linear pair are 135° and 45°

Step-by-step explanation:

They said two angles make a linear pair but the measures of these angles are unknown hence, we take them as 'x'.

One of these angles is one third the other. One third is represented as $\frac{1}{3}$ . It's mentioned it is one third of the other no. but we don't know the measure of the other one (x) hence this one would be $\frac{1}{3} x$=$\frac{x}{3}$ (both are the same as well but I suggest u make it as x by 3 because it makes it a bit more clearer and simpler).

So, these two unknown angles make up a linear pair and we know that a linear pair consists of two angles that make up a straight line that is 180°.

∴$x+\frac{x}{3}$= 180° [linear pair]

Okay, since these two wouldn't go together (I mean add) because they got different denominators, we gotta find the LCM. Since $x$ has the denominator as 1 (numbers without denominator usually have one) (basics of math, if you ask me) (its not necessary to mention one as denominator since one really doesn't have a value) we could just do it directly. It'll be 3 anyway.

$\frac{x}{3}$×$\frac{3}{3}$=$\frac{3x}{3}$

Woohoo! Now we got the same denominators. These guys would surely add now.

$\frac{3x}{3} + \frac{x}{3}$= 180°

$\frac{3x+x}{3}$= 180°

$\frac{4x}{3} =$ 180°

And then, we multiply 180 by 3 because whenever a variable or a number goes or gets transposed to the other side of the equal sign whether LHS to RHS or vice versa, the action that is multiplication, division, addition or if the no. is negative will have the opposite of it.

Multiplication will become division and vice versa.

Addition will become subtraction and vice versa.

Negative will become positive and vice versa.

Square will become square root and vice versa (even cube and all) and so on and so forth if there are more.

That gives 540!

$4x=$ 540°

$x=$$\frac{540}{4}$

$x=$135°

∴ The measures of the angles are 135° and $\frac{135}{3}=$ 45°

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Hope it helps youuuuu!!! :)

Thank you for your question!

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Answer 2

Step-by-step explanation:

Let one angle be x. It is given that other angle is one-third of first.

So, other angle will be x/3.

Again, given that both the angles are making a linear pair.

So, their sum will be 180°

x + x/3 = 180°

(3x + x)/3 = 180°

4x/3 = 180°

x = (180° x 3)/4

x = 135°

Hence, the angles are 135° and 1/3 x 135°, i.e. 135° and 45°.Read more on Sarthaks.com - https://www.sarthaks.com/791874/two-angles-are-making-linear-pair-if-one-of-them-is-one-third-of-the-other-then-find-the-angles