Question

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

Answer 1

• 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.

$\qquad$ $\bf{\underline{\underline{\sf According\ to\ the\ question:-}}}$

$\qquad$$\pink{\bf \twoheadrightarrow {x\ +\ x\ +\ 8°\ =\ 90⁰} }$

$\qquad$$\sf \twoheadrightarrow 2x + 8° = 90°$

$\qquad$$\sf \twoheadrightarrow 2x = 90° - 8°$

$\qquad$$\sf \twoheadrightarrow 2x = 82$

$\qquad$$\sf \twoheadrightarrow x = \cancel{\dfrac{82°}{2}}$

$\qquad$$\pink{\bf \twoheadrightarrow x = 41° }$

Then –

$\qquad$$\bf \longrightarrow x +8°$

$\qquad$$\tt \longrightarrow 41° + 8°$

$\qquad$$\tt \longrightarrow 49°$

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

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