Chapter 2.2, Problem 24PSB

a)

To determine

To calculate: To find P (angles are supplementary)

Answer to Problem 24PSB

0.2

Explanation of Solution

Given information: angles measuring ${30}^{\circ },{60}^{\circ },{150}^{\circ },{45}^{\circ }$ and ${135}^{\circ }$ .

Formula Used: $\text{Probability}=\frac{\text{number of Favourable outcomes}}{\text{total numbers of possible outcomes}}$

Calculation: out of given angles, ${30}^{\circ },{45}^{\circ }$ and ${60}^{\circ }$ are acute angles; ${135}^{\circ }$ and ${150}^{\circ }$ are obtuse.

The chosen angles are supplementary if they are either $({30}^{\circ },{150}^{\circ }),({150}^{\circ },{30}^{\circ }),({45}^{\circ },{135}^{\circ }),({135}^{\circ },{45}^{\circ })$

And they are complementary if they are $({30}^{\circ },{60}^{\circ })$ or $({60}^{\circ },{30}^{\circ })$ .

  $\therefore$ Probability (angles are supplementary) $=\frac{4}{20}=\frac{1}{5}=0.2$

b)

To determine

To calculate: To find P (angles are complementary)

Answer to Problem 24PSB

0.1

Explanation of Solution

Given information: angles measuring ${30}^{\circ },{60}^{\circ },{150}^{\circ },{45}^{\circ }$ and ${135}^{\circ }$ .

Formula Used: $Probability=\frac{numberofFavourable outcomes}{totalnumbersofpossibleoutcomes}$

Calculation: out of given angles, ${30}^{\circ },{45}^{\circ }$ and ${60}^{\circ }$ are acute angles; ${135}^{\circ }$ and ${150}^{\circ }$ are obtuse.

The chosen angles are supplementary if they are either $({30}^{\circ },{150}^{\circ }),({150}^{\circ },{30}^{\circ }),({45}^{\circ },{135}^{\circ }),({135}^{\circ },{45}^{\circ })$

And they are complementary if they are $({30}^{\circ },{60}^{\circ })$ or $({60}^{\circ },{30}^{\circ })$ .

  $\therefore$ Probability (angles are complementary) $=\frac{2}{20}=0.1$