Chapter 10.5, Problem 25PSB

To determine

To Find : $\stackrel{⌢}{AB}$

Answer to Problem 25PSB

$25°$

Explanation of Solution

Given information :

1) $\stackrel{⌢}{SY}=112°$

2) $\stackrel{⌢}{DC}=87°$

Formula Used:

1) Inscribed angle is half of the enclosed arc.

2) The angle between two chords is equal to half the sum of the intercepted arcs.

  $\begin{array}{l}\angle SXY=\frac{1}{2}\stackrel{⌢}{SY}\\ \angle SXY=\frac{1}{2}(112°)\\ \angle SXY=56°\end{array}$

Now

  $\begin{array}{l}\frac{1}{2}(\stackrel{⌢}{DC}+\stackrel{⌢}{AB})=\angle SXY\\ \frac{1}{2}(87°+\stackrel{⌢}{AB})=56°\\ 87°+\stackrel{⌢}{AB}=112\\ \stackrel{⌢}{AB}=25°\end{array}$