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3 years ago

Given:<2=<3 Prove: m<1+<3=180

Mathematics

1 answer:

s2008m [1.1K]3 years ago

7 0

Statement Reason

m<1 + m<2 = 180 linear pair

*(m<1 and "<2 form a straight line together, a straight line has a degree measure of 180)

m<2 = m<3 given

m<1 + m<3 = 180 transitivity

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$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

the given expression can be solved as follows ~

$\frac{x}{13} - 1 = \frac{5x}{2} + \frac{1}{2} \\$

taking LCM both the sides ,

$\frac{x - 13}{13} = \frac{5x + 1}{2} \\$

on cross multiplying ,

$(x - 13)2 = (5x + 1)13 \\ \\ \implies \: 2x - 26 = 65x + 13$

let's now gather the like terms at either sides of the equation ~

$65x - 2x = - 26 - 13 \\ \\ \implies \: 63x = - 39 \\ \\ \implies \: x = \frac{\cancel{ - 39}}{\cancel{63}}$

on simplifying the equation ,

$\implies \frac{-13}{21}\\$

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