Question

what is ( mangle ikj )?
( mangle ikj=square^{circ} )

Explanation:

Step1: Find the value of \(x\)

The sum of angles around a point \(K\) in a circle is \(360^{\circ}\).
So, \((x + 60)+77+(7x - 73)+64 = 360\)
Combine like - terms: \(x+7x+60 + 77-73 + 64=360\)
\(8x+(60 + 77+64 - 73)=360\)
\(8x+(201 - 73)=360\)
\(8x + 128=360\)
Subtract \(128\) from both sides: \(8x=360 - 128\)
\(8x=232\)
Divide both sides by \(8\): \(x=\frac{232}{8}=29\)

Step2: Calculate \(m\angle IKJ\)

Since \(\angle IKJ=x + 60\) and \(x = 29\)
Substitute \(x = 29\) into \(x + 60\): \(m\angle IKJ=29+60\)
\(m\angle IKJ = 89^{\circ}\)

Answer:

\(89\)