Let's analyze the problem step by step.

Problem Analysis

The problem states:

• The supplement of an angle is $60^\circ$ less than twice the supplement of the complement of the angle.

Let:

• $x$ be the measure of the angle.
• The supplement of an angle is $180^\circ - x$.
• The complement of an angle is $90^\circ - x$.
• The supplement of the complement is $180^\circ - (90^\circ - x) = 90^\circ + x$.

Equation Setup

From the problem:

$180^\circ - x = 2(90^\circ + x) - 60^\circ$

Solving the Equation

Let's solve for $x$.

$180^\circ - x = 2(90^\circ + x) - 60^\circ$

Expanding the equation:

$180^\circ - x = 180^\circ + 2x - 60^\circ$

Simplify:

$180^\circ - x = 120^\circ + 2x$

Rearranging terms:

$180^\circ - 120^\circ = 2x + x$

$60^\circ = 3x$

Solving for $x$:

$x = 20^\circ$

Finding the Complement

The complement of the angle is:

$90^\circ - x = 90^\circ - 20^\circ = 70^\circ$

Conclusion

The measure of the complement of the angle is 70 degrees.

Would you like more details, or do you have any questions?

Related Questions:

1. What is the difference between complementary and supplementary angles?
2. How do you find the supplement of an angle if you know its measure?
3. Can you have an angle that is both complementary and supplementary to another angle?
4. How would the problem change if it involved exterior angles of a polygon?
5. How can you solve angle-related problems involving more complex geometric figures?

Tip:

Always remember that complementary angles add up to $90^\circ$ and supplementary angles add up to $180^\circ$. This is useful for quickly setting up equations!