The complement of an angle is (24^\circ) more than the angle. What is the angle?
Answer and explanation
Correct answer: \(33^\circ\)
Let the angle be \(x^\circ\). Its complement is \((90-x)^\circ\). Given that the complement is \(24^\circ\) greater than the angle, \(90-x=x+24\). Thus, \(2x=66\), so \(x=33\). Therefore, the correct answer is \(33^\circ\). For example, if the angle were \(36^\circ\), its complement would be \(54^\circ\), which is only \(18^\circ\) greater. Exam tip: complementary angles always add up to \(90^\circ\).
Frequently asked questions
What is the correct answer to this question?
\(33^\circ\)
Why is this the correct answer?
Let the angle be \(x^\circ\). Its complement is \((90-x)^\circ\). Given that the complement is \(24^\circ\) greater than the angle, \(90-x=x+24\). Thus, \(2x=66\), so \(x=33\). Therefore, the correct answer is \(33^\circ\). For example, if the angle were \(36^\circ\), its complement would be \(54^\circ\), which is only \(18^\circ\) greater. Exam tip: complementary angles always add up to \(90^\circ\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
