Question

question 7 (1 point) determine whether the two angles shown are complementary, supplementary, or neither. a complementary b supplementary c neither

Explanation:

Step1: Calculate the first - clock angle

The first clock shows 12:15. The minute - hand is at 3 and the hour - hand has moved $\frac{15}{60}=\frac{1}{4}$ of the way between 12 and 1. Each hour on the clock represents an angle of $30^{\circ}$ (since $360\div12 = 30^{\circ}$). The angle of the first clock is $90^{\circ}$.

Step2: Calculate the second - clock angle

The second clock shows 5:45. The minute - hand is at 9 and the hour - hand has moved $\frac{45}{60}=\frac{3}{4}$ of the way between 5 and 6. The position of the hour - hand from 12 is $5\times30^{\circ}+ \frac{3}{4}\times30^{\circ}=150^{\circ}+ 22.5^{\circ}=172.5^{\circ}$, and the minute - hand is at $9\times30^{\circ}=270^{\circ}$. The angle between the hands is $270^{\circ}-172.5^{\circ}=97.5^{\circ}$.

Step3: Check the relationship

Complementary angles add up to $90^{\circ}$, and supplementary angles add up to $180^{\circ}$. The sum of the two angles $90^{\circ}+97.5^{\circ}=187.5^{\circ}$. So they are neither complementary nor supplementary.

Answer:

c. neither