Answer:
Let the angles be x and y
So, x + y = 180° - (1)
x = y +18
→ y + 18+ y = 180°
..y = 81; x = 99°
Let,
[tex]\mapsto \bf Smaller\: Angle_{(Supplementary\: Angle)} =\: x\\[/tex]
[tex]\mapsto \bf Larger\: Angle_{(Supplementary\: Angle)} =\: x + 18^{\circ}\\[/tex]
As we know that :
[tex]\small \bigstar \: \: \sf\boxed{\bold{Sum\: Of\: Two\: Angles_{(Supplementary\: Angles)} =\: 180^{\circ}}}\: \: \: \bigstar\\[/tex]
According to the question by using the formula we get,
[tex]\small \implies \sf\boxed{\bold{\bigg\{Smaller\: Angle_{(Supplementary\: Angle)}\bigg\} + \bigg\{Larger\: Angle_{(Supplementary\: Angle)}\bigg\} =\: 180^{\circ}}}\\[/tex]
[tex]\implies \sf x + x + 18^{\circ} =\: 180^{\circ}\\[/tex]
[tex]\implies \sf 2x + 18^{\circ} =\: 180^{\circ}\\[/tex]
[tex]\implies \sf 2x =\: 180^{\circ} - 18^{\circ}\\[/tex]
[tex]\implies \sf 2x =\: 162^{\circ}\\[/tex]
[tex]\implies \sf x =\: \dfrac{162^{\circ}}{2}\\[/tex]
[tex]\implies \sf\bold{x =\: 81^{\circ}}\\[/tex]
Hence, the required angles of supplementary angles are :
[tex]\dag[/tex] Smaller Angle Of Supplementary Angle :
[tex]\dashrightarrow \sf Smaller\: Angle_{(Supplementary\: Angle)} =\: x\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Smaller\: Angle_{(Supplementary\: Angle)} =\: 81^{\circ}}}\\[/tex]
[tex]\dag[/tex] Larger Angle Of Supplementary Angle :
[tex]\dashrightarrow \sf Larger\: Angle_{(Supplementary\: Angle)} =\: x + 18^{\circ}\\[/tex]
[tex]\dashrightarrow \sf Larger\: Angle_{(Supplementary\: Angle)} =\: 81^{\circ} + 18^{\circ}\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Larger\: Angle_{(Supplementary\: Angle)} =\: 99^{\circ}}}\\[/tex]
[tex]\therefore[/tex] The two angles of supplementary angles are 81° and 99° respectively.
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Answers & Comments
Answer:
Let the angles be x and y
So, x + y = 180° - (1)
x = y +18
→ y + 18+ y = 180°
..y = 81; x = 99°
Verified answer
Answer:
Given :-
To Find :-
Solution :-
Let,
[tex]\mapsto \bf Smaller\: Angle_{(Supplementary\: Angle)} =\: x\\[/tex]
[tex]\mapsto \bf Larger\: Angle_{(Supplementary\: Angle)} =\: x + 18^{\circ}\\[/tex]
As we know that :
[tex]\small \bigstar \: \: \sf\boxed{\bold{Sum\: Of\: Two\: Angles_{(Supplementary\: Angles)} =\: 180^{\circ}}}\: \: \: \bigstar\\[/tex]
According to the question by using the formula we get,
[tex]\small \implies \sf\boxed{\bold{\bigg\{Smaller\: Angle_{(Supplementary\: Angle)}\bigg\} + \bigg\{Larger\: Angle_{(Supplementary\: Angle)}\bigg\} =\: 180^{\circ}}}\\[/tex]
[tex]\implies \sf x + x + 18^{\circ} =\: 180^{\circ}\\[/tex]
[tex]\implies \sf 2x + 18^{\circ} =\: 180^{\circ}\\[/tex]
[tex]\implies \sf 2x =\: 180^{\circ} - 18^{\circ}\\[/tex]
[tex]\implies \sf 2x =\: 162^{\circ}\\[/tex]
[tex]\implies \sf x =\: \dfrac{162^{\circ}}{2}\\[/tex]
[tex]\implies \sf\bold{x =\: 81^{\circ}}\\[/tex]
Hence, the required angles of supplementary angles are :
[tex]\dag[/tex] Smaller Angle Of Supplementary Angle :
[tex]\dashrightarrow \sf Smaller\: Angle_{(Supplementary\: Angle)} =\: x\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Smaller\: Angle_{(Supplementary\: Angle)} =\: 81^{\circ}}}\\[/tex]
[tex]\dag[/tex] Larger Angle Of Supplementary Angle :
[tex]\dashrightarrow \sf Larger\: Angle_{(Supplementary\: Angle)} =\: x + 18^{\circ}\\[/tex]
[tex]\dashrightarrow \sf Larger\: Angle_{(Supplementary\: Angle)} =\: 81^{\circ} + 18^{\circ}\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Larger\: Angle_{(Supplementary\: Angle)} =\: 99^{\circ}}}\\[/tex]
[tex]\therefore[/tex] The two angles of supplementary angles are 81° and 99° respectively.