Question

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

Answer 1

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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${\longrightarrow \qquad \sf{ x = \dfrac{116.8^{ \circ}}{2}}}$

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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° .