Question

if m∠ihj is 72°, what is m∠ijh? the vertices of triangle hij lie on circle k, as shown.

Explanation:

Step1: Recall inscribed - angle property

In a circle, angles inscribed in the same arc are equal. Here, \(\angle IHJ\) and \(\angle IJH\) are inscribed angles that intercept the same arc \(\overset{\frown}{IH}\).

Step2: Use given angle measure

We know that \(m\angle IHJ = 72^{\circ}\). Since \(\angle IHJ\) and \(\angle IJH\) are equal (angles inscribed in the same arc), \(m\angle IJH=m\angle IHJ\).

Answer:

\(72^{\circ}\)