Since the vertices of triangle HIJ lie on circle K, the measure of m∠IJH is: A.18°.
By critically observing the diagram, we can logically deduce that line segment HJ represents the diameter of circle K. Since line segment HJ is the diameter of circle K, the measure of angle HIJ must be a right angle;
m∠HIJ = 90°.
In Mathematics and Geometry, the sum of the interior angles in a triangle is equal to 180 degrees. This ultimately implies that, we would sum up all of the angles in triangle HIJ as follows;
m∠HIJ + m∠IHJ + m∠IJH = 180°
90 + 72 + m∠IJH = 180°
162 + m∠IJH = 180°
m∠IJH = 180° - 162
m∠IJH = 18°
Complete Question;
The vertices of triangle HIJ lie on circle K, as shown. If m∠IHJ is 72°, what is m∠IJH? 18° 45° 108° 198°