Answer:
[tex]m\angle 1=27^{\circ}[/tex]
Step-by-step explanation:
We have been given a circle in which secants GH and GK intersecting to form an angle. We are asked to find the measure of angle 1.
We know that the measure of angle formed by two intersecting secants outside the circle is half the difference of intercepted arcs.
[tex]m\angle 1=\frac{\widehat{KH}-\widehat{JI}}{2}[/tex]
[tex]m\angle 1=\frac{83^{\circ}-29^{\circ}}{2}[/tex]
[tex]m\angle 1=\frac{54^{\circ}}{2}[/tex]
[tex]m\angle 1=27^{\circ}[/tex]
Therefore, the measure of angle 1 is 27 degrees.
