Question

find the measure of ∠ilj. write your answer as a whole number or a decimal. m∠ilj =

Explanation:

Step1: Recall circle - angle property

The sum of the central - angles of a circle is 360°.

Step2: Set up an equation

Let \(m\angle ILJ=x\). We know that \(67^{\circ}+89^{\circ}+m\angle HLJ + m\angle ILJ=360^{\circ}\). Since vertical angles are equal, and we assume the angles formed by the intersecting lines at the center of the circle, and we know that the non - given angles are also part of the 360 - degree sum. If we consider the two given angles \(67^{\circ}\) and \(89^{\circ}\), and assume the other two angles are \(m\angle HLJ\) and \(m\angle ILJ\) (where \(m\angle HLJ\) and the non - given angle adjacent to \(67^{\circ}\) are vertical, and \(m\angle ILJ\) and the non - given angle adjacent to \(89^{\circ}\) are vertical). In a circle, the sum of all central angles is 360°. Also, vertical angles are equal. So \(m\angle ILJ=\frac{1}{2}(360-(67 + 89))\).

Step3: Calculate the value

First, calculate the sum of the given angles: \(67+89 = 156\). Then, \(360-156=204\). And \(m\angle ILJ=\frac{204}{2}=102\).

Answer:

\(102\)