Question

question d (11 points)
if ( overline{km} ) and ( overline{lm} ) are tangent segments, what is the measure of ( angle kml )?
the measurement of ( angle kml=)______(^{circ})
blank 1:

Explanation:

Step1: Recall the property of tangent - radius

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \(\angle OKM=\angle OLM = 90^{\circ}\)

Step2: Use the sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral \(OKML\) is \(360^{\circ}\). Let \(\angle KML=x\) and \(\angle KOL = 63^{\circ}\) (given).
We know that \(\angle OKM+\angle KML+\angle OLM+\angle KOL=360^{\circ}\)
Substitute \(\angle OKM = 90^{\circ}\), \(\angle OLM=90^{\circ}\) and \(\angle KOL = 63^{\circ}\) into the equation:
\(90^{\circ}+x + 90^{\circ}+63^{\circ}=360^{\circ}\)
\(x+243^{\circ}=360^{\circ}\)
\(x=\angle KML=360^{\circ}- 243^{\circ}=54^{\circ}\)

Answer:

54