Question

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

Answer 1

The measurement of each angle is 58.4° and 31.6°

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

Answer 2

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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`{\longrightarrow \qquad \sf{ x + {(x - 26.8)}^( \circ) = {90}^( \circ) }}`

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`{\longrightarrow \qquad \sf{ x + {x - 26.8}^( \circ) = {90}^( \circ) }}`

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`{\longrightarrow \qquad \sf{ 2 {x - 26.8}^( \circ) = {90}^( \circ) }}`

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`{\longrightarrow \qquad \sf{ 2 x = {90}^( \circ) + 26.8^( \circ)}}`

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`{\longrightarrow \qquad \sf{ 2 x = 116.8^( \circ)}}`

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`{\longrightarrow \qquad \sf{ x = (116.8^( \circ))/(2)}}`

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`{\longrightarrow \qquad \frak{\pmb{ x =58.4^( \circ)}}}`

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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° .