Question

The difference between the measures of two angles of a linear pair is 80°. Find
the measure of each angle.

Answer 1

Given: The Difference b/w the measure of two angles of a linear pair is 80°.

Need to find: The measure of each angle?

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❍ Let's Consider that the two angles be x and y respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀

• Sum of Linear pair angles is 180°. Therefore:

$:\implies\sf x + y = 180^\circ$

$:\implies\sf y = 180^\circ - x\qquad\qquad\qquad\Bigg\lgroup\sf eq^n \;(1)\Bigg\rgroup$

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${\underline{\bigstar\;{\boldsymbol{According\: to \:the\: Question~ :}}}}$

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• The Difference b/w the measure of two angles of a linear pair is 80°.

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$\twoheadrightarrow\sf\quad x - y = 80^\circ$

$\twoheadrightarrow\sf\quad x - 180^\circ - x = 80^\circ\qquad\qquad\qquad\Bigg\lgroup\sf From\;eq^n \;(1)\Bigg\rgroup$

$\twoheadrightarrow\sf\quad x - 180^\circ + x = 80^\circ$

$\twoheadrightarrow\sf\quad 2x = 260^\circ$

$\twoheadrightarrow\sf\quad x = \cancel\dfrac{260^\circ}{2}$

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{x = 130^\circ}}}}\;\bigstar$

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Therefore,

• First angle, x = 130°
• Second angle, y = 180° – x = y = 180° – 130° = y = 50°

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❝ Hence, the angles are 50° and 130° respectively. ❞

Answer 2

Given :-

The difference between the measures of two angles of a linear pair is 80°

To Find :-

Find  the measure of each angle.

Solution :-

Let the first angle be x

Second angle = (180 - x)

Their difference is 80

(180 - x) - (x) = 80

180 - x - x = 80

- x - x = 80 - 180

-2x = -100

x = -100/-2

x = 100/2

x = 50

Hence,

Angles are

x = 50

180 - x = 180 - 50 = 130