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Ede4ka [16]
2 years ago
8

An angle measures 13.8° more than the measure of its complementary angle. What is the measure of each angle?

Mathematics
1 answer:
prohojiy [21]2 years ago
8 0
<h3>First let us know –</h3>

  • 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.<u>Example</u> : 60° and 30° are two angles, and their sum is 90°. So, 60° and 30° are complementary angles.

\qquad____________________

<h3><u>Explanation</u> :-</h3>

  • 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!

<h3><u>Solution</u> :-</h3>

  • 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.

\bf{\underline{\underline{\dag According\ to\ the\ question:-}}}

\qquad\pink{\bf\longrightarrow  {x\ +\ x\ +\ 13.8°\ =\ 90⁰}  }

\qquad\sf \longrightarrow 2x + 13.8° = 90°

\qquad\sf \longrightarrow 2x = 90° - 13.8°

\qquad\sf \longrightarrow 2x = 76.2°

\qquad\sf \longrightarrow x = \cancel{\dfrac{76.2°}{2}}

\qquad\pink{\bf \longrightarrow x = 38.1° }

<u>Then</u> –

\qquad\bf  \longrightarrow x +13.8°

\qquad\tt \longrightarrow   38.1° + 13.8°

\qquad\tt \longrightarrow 51.9°

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

\qquad______________________

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