Question

find m∠a. m∠a = ° submit

Explanation:

Step1: Calculate the measure of arc \(AB\)

The sum of the measures of the arcs of a circle is \(360^{\circ}\).
Let the measure of arc \(AB\) be \(x\). Then \(x + 102^{\circ}+60^{\circ}+93^{\circ}=360^{\circ}\)
\(x=360^{\circ}-(102^{\circ}+60^{\circ}+93^{\circ})\)
\(x = 360^{\circ}-255^{\circ}\)
\(x = 105^{\circ}\)

Step2: Use the formula for the measure of an inscribed quadrilateral related to arcs

The measure of an inscribed angle \(A\) in a circle (where \(A\) is an angle of a cyclic quadrilateral \(ABCD\)) is given by \(m\angle A=\frac{1}{2}(m\overset{\frown}{DC}+m\overset{\frown}{BC})\). Another way (using the sum of opposite angles of a cyclic quadrilateral and the property of angles and arcs).
The measure of an inscribed angle is half the measure of its intercepted arc. For a cyclic quadrilateral \(ABCD\) inscribed in a circle, \(m\angle A=\frac{1}{2}(m\overset{\frown}{BCD})\)
\(m\overset{\frown}{BCD}=102^{\circ}+60^{\circ}=162^{\circ}\)
\(m\angle A=\frac{1}{2}(162^{\circ})\)

Answer:

\(81\)