The complement of an angle exceeds the angle by 60°. Then the angle is equal to -

Explanation for Complement of an Angle Exceeds the Angle by 60° Problem

The given problem states:

The complement of an angle exceeds the angle by 60°. Then the angle is equal to -

The available choices are:

• 15°

• 25°

• 30°

• 35°

The correct answer is 15°. Here is a detailed explanation:

Understanding Complementary Angles

Two angles are said to be complementary if the sum of their measures is 90°. This can be mathematically expressed as:

$ \theta + \phi = 90^\circ $

Where \( \theta \) and \( \phi \) are the measures of the two complementary angles.

Formulating the Problem

According to the problem, the complement of an angle exceeds the angle by 60°. Let’s denote the angle by \( x \); then its complement will be \( 90^\circ - x \). The problem states the following relationship:

$ (90^\circ - x) = x + 60^\circ $

We need to solve for \( x \).

Solving the Equation

Let's solve the equation step-by-step:

1. Start with the given equation:

   $ 90^\circ - x = x + 60^\circ $

2. Rearrange the equation to isolate \( x \):

   $ 90^\circ - 60^\circ = x + x $

3. Simplify the left-hand side:

   $ 30^\circ = 2x $

4. Solve for \( x \):

   $ x = \frac{30^\circ}{2} = 15^\circ $

Conclusion:

Therefore, the angle that satisfies the condition is \( x = 15^\circ \). This can be verified by substituting back into the original condition:

$ 90^\circ - 15^\circ = 75^\circ $

and checking:

$ 75^\circ = 15^\circ + 60^\circ $

This equality holds true, confirming that the angle is indeed 15°.

Thus, the correct answer is 15°.