원의 성질 - 원주각의 크기 구하기

문제

다음 그림과 같이 원의 중심이 $\mathrm{O}$이고, $\overset{\frown}{\mathrm{AB}}$에 대한 중심각 $\angle \mathrm{AOB}$의 크기가 $80^\circ$일 때, $\overset{\frown}{\mathrm{AB}}$에 대한 원주각 $\angle \mathrm{APB}$의 크기는 얼마인가요? (단, 점 $\mathrm{P}$는 원 위의 한 점입니다.)

<!-- Lines OA, OB, PA, PB -->
<line x1="200" y1="150" x2="113.40" y2="100.00"/> <!-- OA -->
<line x1="200" y1="150" x2="234.20" y2="56.03"/> <!-- OB -->
<line x1="300.00" y1="150.00" x2="113.40" y2="100.00"/> <!-- PA -->
<line x1="300.00" y1="150.00" x2="234.20" y2="56.03"/> <!-- PB -->

<!-- Angle Arcs -->
<!-- Arc for Angle AOB (80 degrees) -->
<!-- Path from a point on OB to a point on OA, with center O, counter-clockwise sweep -->
<path d="M 208.55 126.51 A 25 25 0 0 1 178.35 137.50"/>
<!-- Arc for Angle APB (?) -->
<!-- Path from a point on PA to a point on PB, with center P, counter-clockwise sweep -->
<path d="M 275.85 156.47 A 25 25 0 0 1 285.66 170.48"/>

<!-- Points -->
<circle cx="200" cy="150" r="3" fill="#1F2937"/> <!-- O -->
<circle cx="113.40" cy="100.00" r="3" fill="#1F2937"/> <!-- A -->
<circle cx="234.20" cy="56.03" r="3" fill="#1F2937"/> <!-- B -->
<circle cx="300.00" cy="150.00" r="3" fill="#1F2937"/> <!-- P -->

<!-- Labels for Points -->
<text x="195" y="165" text-anchor="end" fill="#1F2937">O</text> <!-- O -->
<text x="100" y="95" text-anchor="end" fill="#1F2937">A</text> <!-- A -->
<text x="235" y="45" text-anchor="start" fill="#1F2937">B</text> <!-- B -->
<text x="305" y="155" text-anchor="start" fill="#1F2937">P</text> <!-- P -->

<!-- Labels for Angles -->
<text x="188.03" y="117.11" text-anchor="middle" font-size="16" dy="5" fill="#1F2937">80°</text> <!-- Angle AOB -->
<text x="271.33" y="170.08" text-anchor="middle" font-size="16" dy="5" fill="#1F2937">?</text> <!-- Angle APB -->