Given :
- An angle which measures less 64° the measure of its supplementary angle.
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To Find :
- The measure of its supplementary angle.
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Solution :
- Let's assume the one of the supplementary angle as x and the other angle as (x - 64)° .
Now,
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According to the Question :
[tex]\longrightarrow\qquad \sf{{x
+ (x - 64) {}^{ \circ} = {180}^{ \circ} }}[/tex]
[tex]\longrightarrow\qquad \sf{{x + x - 64 {}^{ \circ} = {180}^{ \circ} }}[/tex]
[tex]\longrightarrow\qquad \sf{{2x - 64 {}^{ \circ} = {180}^{ \circ} }}[/tex]
[tex]\longrightarrow\qquad \sf{{2x = {180}^{ \circ} + 64 {}^{ \circ}}}[/tex]
[tex]\longrightarrow\qquad \sf{{2x = {244}^{ \circ} }}[/tex]
[tex]\longrightarrow\qquad \sf{{x = \dfrac{{244}^{ \circ}}{2} }}[/tex]
[tex]\longrightarrow\qquad \mathfrak{\pmb{{x = {122}^{ \circ} }}}[/tex]
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Therefore,
- One angle = 122°
- Other angle = 122° – 64° = 58°
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Henceforth ,
- The measure of the two angles are 122° and 58° .
