Chapter 11.1, Problem 31PPS

a)

To determine

To find: $m\angle WXY$ and $m<YXZ$ .

Answer to Problem 31PPS

  $m\angle WXY={60}^{{}^0}$ and $\angle YXZ={120}^0$.

Explanation of Solution

Given information: The following clock, showing 6 o`clock and 10 seconds.

  

Concept used: The line segment WZ forms a straight angle here, so that the angle formed at point X is 180 degree. Thus, there is a gap of 2 hours between WX and XY and there is a gap of 4 hours between XY and XZ.

Calculation: By figure, a needle of hour from W to Z, cover 6 hours, so, the angle between two needles, showing one hour:

  $=\frac{180}{6}={30}^0$

So, $m\angle WXY=2\times 30°=60°$

And $m\angle YXZ=4\times 30°=120°$

Also, when $m\angle WXY=m\angle YXZ={90}^0$

Then the needle XY (showing seconds) will be at 3 hours.

Conclusion: Clearly $m\angle WXY={60}^{{}^0}$and $\angle YXZ={120}^0$.

b)

To determine

To find: The time when $m\angle WXY=m\angle YXZ={90}^0$

Answer to Problem 31PPS

The time when $m\angle WXY=m\angle YXZ={90}^0$ is 6 o`clock, 15 seconds.

Explanation of Solution

Given information: Following clock, showing 6 o`clock and 10 seconds.

  

Concept used: Line segment WZ forms a straight angle here, so that the angle formed at point X is 180 degree. Also, there is a gap of 2 hours between WX and XY and there is a gap of 4 hours between XY and XZ.

Calculation: By figure, a needle of hour from W to Z, cover 6 hours, so, the angle between two needles, showing one hour,

  $=\frac{180}{6}={30}^0$

So, $m\angle WXY=2\times 30°=60°$

And $m\angle YXZ=4\times 30°=120°$

Also, when $m\angle WXY=m\angle YXZ={90}^0$

Then the needle XY (showing seconds) will be at 3 hours.

Conclusion: Needle XY as will be at 3 hours, time when $m\angle WXY=m\angle YXZ={90}^0$ will be 6 o`clock, 15 seconds.