Question

An angle measures 64° less than the measure of its supplementary angle what is the measure of each angle

Answer 1

Given :

• An angle which measures less 64° the measure of its supplementary angle.

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To Find :

• The measure of its supplementary angle.

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Solution :

• Let's assume the one of the supplementary angle as x and the other angle as (x - 64)° .

Now,

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According to the Question :

`\longrightarrow\qquad \sf{{x </p><p> + (x - 64) {}^( \circ) = {180}^( \circ) }}`

`\longrightarrow\qquad \sf{{x + x - 64 {}^( \circ) = {180}^( \circ) }}`

`\longrightarrow\qquad \sf{{2x - 64 {}^( \circ) = {180}^( \circ) }}`

`\longrightarrow\qquad \sf{{2x = {180}^( \circ) + 64 {}^( \circ)}}`

`\longrightarrow\qquad \sf{{2x = {244}^( \circ) }}`

`\longrightarrow\qquad \sf{{x = \frac{{244}^( \circ)}{2} }}`

`\longrightarrow\qquad \mathfrak{\pmb{{x = {122}^( \circ) }}}`

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Therefore,

• One angle = 122°
• Other angle = 122° – 64° = 58°

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Henceforth ,

• The measure of the two angles are 122° and 58° .