Respuesta :
Step-by-step explanation:
Finally complement of the supplement of twice the angle 60°=90°-60°=30
60 degrees angle is an acute angle because it is less than 90 degrees. 60° in radians is π/3 and the measure of each angle of an equilateral triangle is 60°. Therefore, it is also called a 60-degree angle triangle.
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Given :
- An angle which measures less 60° the measure of its complementary angle.
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To Find :
- The measure of its complementary angle.
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Solution :
Let's assume the one of the complementary angle as "x" and the other angle as (x - 60)° .
Now,
According to the Question :
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + (x - 60) {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + (x - 60) {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + x {}^{ \circ} - 60 {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{{2x}^{ \circ} = {90}^{ \circ} + 60 {}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{{2x}^{ \circ} = 150 {}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x = \dfrac{150 {}^{ \circ}}{2 {}^{ \circ}} }}
[/tex]
[tex]\: \qquad \dashrightarrow \bf{{{x}^{ \circ} = 75 {}^{ \circ} }}
[/tex]
Therefore,
- One angle = 75°
- Other angle = 75° – 60° = 15°
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Henceforth ,
The measure of the two angles are 75° and 15° .
