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Option 3 : 186°
Given:
Complementary angle = 7 × original angle - 6°
Concept Used:
Complementary Angles: The pair of angles whose sum is equal to 90° are called Complementary Angles.
Supplementary Angles: The pair of angles whose sum is equal to 180° are called Supplementary Angles.
Calculations:
Let the original angle be x.
According to the question,
Complementary angle of x = 7x - 6
90 - x = 7x - 6
⇒ 8x = 96
⇒ x = 96/8
⇒ x = 12°
Now, Supplementary angle of x = 180° - x
⇒ 180° - 12° = 168°
According to the question, required angle = 168° + 18°
⇒ 186°
∴ The measure of the required angle is 186°.
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