Chapter 10, Problem 18RP

a)

To determine

To find : the value of $\angle X$

Answer to Problem 18RP

  $\angle X=140°$

Explanation of Solution

Given Information :

We know that, $\stackrel{⌢}{AB}=30°,\stackrel{⌢}{BC}=40°$ and $\stackrel{⌢}{CD}=50°$ .

  

Formula Used:

Outside Angle Theorem : Angle formed by two tangents outside a circle is equal to half of the difference of intercepted arcs.

Calculation :

  $\angle X=\frac{((240°+50°+30°)-40)}{2}=140°$

b)

To determine

To find : the value of $\angle Y$

Answer to Problem 18RP

  $\angle Y=30°$

Explanation of Solution

Given Information :

We know that, $\stackrel{⌢}{AB}=30°,\stackrel{⌢}{BC}=40°$ and $\stackrel{⌢}{CD}=50°$ .

Formula Used:

Outside Angle Theorem : Angle formed by two tangents outside a circle is equal to half of the difference of intercepted arcs.

Calculation :

  $\angle Y=\frac{((50°+40°)-30°)}{2}=30°$

c)

To determine

To find : the value of $\angle Z$

Answer to Problem 18RP

  $\angle Z=10°$

Explanation of Solution

Given Information :

We know that $\stackrel{⌢}{AB}=30°,\stackrel{⌢}{BC}=40°$ and $\stackrel{⌢}{CD}=50°$ .

Formula Used:

Outside Angle Theorem : Angle formed by two tangents outside a circle is equal to half of the difference of intercepted arcs.

Calculation :

  $\angle Z=(180°-(140°+30°))=10°$