Chapter 3, Problem 18CR

To determine

To calculate: The measure of half of the complement.

Answer to Problem 18CR

The measure of half of the complement is ${25}^{\circ }$

Explanation of Solution

Given information: The measure is the supplement of an angle exceeds twice the measure of the complement of the angle by $40$ is provided in the question which will help to find the solution.

Formula used: For Supplement = ${180}^{\circ }-x$ and for Complement = ${90}^{\circ }-x$

Calculation: Let the angle be x, supplement be S and complement be C

Now, according to question

  →$S=2C+40$

  →${180}^{\circ }-x=2\left({90}^{\circ }-x\right)+40$

  →${180}^{\circ }-x={180}^{\circ }-2x+40$

So, $x={40}^{\circ }$

Now, complement = ${90}^{\circ }-x$

  →${90}^{\circ }-{40}^{\circ }$

  →${50}^{\circ }$

Now, $\frac{C}{2}={25}^{\circ }$

Conclusion: Hence, the measure of half of the complement is ${25}^{\circ }$