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First let us know –

  • 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 13.8° 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 + 13.8)° "

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

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

[tex]\qquad[/tex][tex] \pink{\bf\longrightarrow {x\ +\ x\ +\ 13.8°\ =\ 90⁰} }[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 2x + 13.8° = 90° [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 2x = 90° - 13.8° [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 2x = 76.2° [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow x = \cancel{\dfrac{76.2°}{2}} [/tex]

[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow x = 38.1° }[/tex]

Then –

[tex]\qquad[/tex][tex] \bf \longrightarrow x +13.8° [/tex]

[tex]\qquad[/tex][tex] \tt \longrightarrow 38.1° + 13.8° [/tex]

[tex]\qquad[/tex][tex] \tt \longrightarrow 51.9° [/tex]

  • The measures of the two given angles is 38.1° and 51.9°.

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