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An angle measures 26.8° less than the measure of its complementary angle. What is the measure of each angle?

An Angle Measures 268 Less Than The Measure Of Its Complementary Angle What Is The Measure Of Each Angle class=

Sagot :

Given :

  • An angle which measures 26.8° less than the measure of its complementary angle.

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To Find :

  • The measure of each angle.

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Solution :

  • Let's assume the one of the complementary angle as "x" and the other angle as (x – 26.8)° .

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Now,

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According to the Question :

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[tex]{\longrightarrow \qquad \sf{ x + {(x - 26.8)}^{ \circ} = {90}^{ \circ} }}[/tex]

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[tex]{\longrightarrow \qquad \sf{ x + {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]

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[tex]{\longrightarrow \qquad \sf{ 2 {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]

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[tex]{\longrightarrow \qquad \sf{ 2 x = {90}^{ \circ} + 26.8^{ \circ}}}[/tex]

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[tex]{\longrightarrow \qquad \sf{ 2 x = 116.8^{ \circ}}}[/tex]

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[tex]{\longrightarrow \qquad \sf{ x = \dfrac{116.8^{ \circ}}{2}}}[/tex]

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[tex]{\longrightarrow \qquad \frak{\pmb{ x =58.4^{ \circ}}}}[/tex]

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Therefore,

  • One angle = 58.4°

  • Other angle = 58.4° – 26.8° = 31.6°

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Hence,

  • The measure of the each angles are 58.4° and 31.6° .
SupremeStrange

Answer:

The measurement of each angle is 58.4° and 31.6°

Step-by-step explanation:

Given :-

  • Value of an angle is 26.8° less than its complementary angle

To Find :-

  • Measurement of each angle

Solution:-

let one angle be x and other be x - 26.8°

we know that, Sum of complementary angle is 90°

X + X - 26.8° = 90°

2x = 90° + 26.8°

x = 58.4

So , one angle is 58.4° and other one is 58.4 - 26.8 which is 31.6

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