Question

what are the measures of angles 1 and 2?
$m\angle1=\square{\circ}$
$m\angle2=\square{\circ}$

Explanation:

Step1: Use the formula for the measure of an angle formed by two intersecting chords

The formula is \(m\angle=\frac{1}{2}(m\overset{\frown}{arc_1} + m\overset{\frown}{arc_2})\). For \(\angle1\), \(m\overset{\frown}{RQ}=53^{\circ}\) and \(m\overset{\frown}{TS} = 47^{\circ}\).
\(m\angle1=\frac{1}{2}(53^{\circ}+ 47^{\circ})\)

Step2: Calculate \(m\angle1\)

\(m\angle1=\frac{1}{2}(100^{\circ})=50^{\circ}\)

Step3: Use the property of vertical angles

\(\angle1\) and \(\angle2\) are vertical angles. Vertical angles are equal. So \(m\angle2=m\angle1\)

Answer:

\(m\angle1 = 50^{\circ}\)
\(m\angle2 = 50^{\circ}\)