Question

question find ( m angle i k j ). answer attempt 1 out of 2 ( m angle i k j= )

Explanation:

Step1: Recall the property of isosceles triangle

In \(\triangle IJK\), since \(IJ = JK\) (marked with the same symbol), \(\triangle IJK\) is isosceles. The sum of interior angles of a triangle is \(180^{\circ}\). Let \(m\angle IKJ=m\angle JIK = x\).

Step2: Set up the equation

We know that \(m\angle J+ m\angle IKJ+m\angle JIK=180^{\circ}\). Substitute \(m\angle J = 121^{\circ}\) and \(m\angle IKJ=m\angle JIK = x\) into the equation: \(121^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation

Simplify the equation \(121 + 2x=180\). First, subtract \(121\) from both sides: \(2x=180 - 121=59\). Then divide both sides by \(2\): \(x=\frac{59}{2}=29.5\)

Answer:

\(29.5\)