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An angle measures 8° more than the measure of its complementary angle. What is the measure of each angle?

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  • What is complementary angle ?

  • When sum of two angles is 90°, then each of those two angles will be considered to be the complementary angle of each other.Example : 60° and 30° are two angles, and their sum is 90°. So, 60° and 30° are complementary angles.

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Explanation :-

  • Measure of an angle is 8° more than the measure of it's complementary angle. We are asked to find measure of each angle!

Solution :-

  • One of the complementary angles be "x" . Then the other angle becomes " (x + 8)° "

  • Sum of these two angles is equal to 90° . Since they are complementary angles.

[tex]\qquad[/tex] [tex] \bf{\underline{\underline{\sf According\ to\ the\ question:-}}} [/tex]

[tex]\qquad[/tex][tex] \pink{\bf \twoheadrightarrow {x\ +\ x\ +\ 8°\ =\ 90⁰} }[/tex]

[tex]\qquad[/tex][tex] \sf \twoheadrightarrow 2x + 8° = 90° [/tex]

[tex]\qquad[/tex][tex] \sf \twoheadrightarrow 2x = 90° - 8° [/tex]

[tex]\qquad[/tex][tex] \sf \twoheadrightarrow 2x = 82 [/tex]

[tex]\qquad[/tex][tex] \sf \twoheadrightarrow x = \cancel{\dfrac{82°}{2}} [/tex]

[tex]\qquad[/tex][tex] \pink{\bf \twoheadrightarrow x = 41° }[/tex]

Then –

[tex]\qquad[/tex][tex] \bf \longrightarrow x +8° [/tex]

[tex]\qquad[/tex][tex] \tt \longrightarrow 41° + 8° [/tex]

[tex]\qquad[/tex][tex] \tt \longrightarrow 49° [/tex]

  • The measures of the two given angles are 41° and 49°.

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