Question

question
in the diagram below, find ( moverline{hk} ).
answer attempt 2 out of 2
additional solution no solution
( hk=) units submit answer

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(2x - 8=127 - x\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides: \(2x+x - 8=127 - x+x\), \(3x - 8 = 127\).
Add \(8\) to both sides: \(3x-8 + 8=127 + 8\), \(3x=135\).
Divide both sides by \(3\): \(x=\frac{135}{3}=45\).

Step3: Find the measure of \(\angle JMH\)

Substitute \(x = 45\) into \(2x - 8\): \(2\times45-8=90 - 8 = 82^{\circ}\).
Since \(MN\perp HJ\) (right - angle at \(N\)), the central angle corresponding to \(\widehat{HK}\) is \(90+(127 - x)\).
Substitute \(x = 45\) into \(127 - x\): \(127-45 = 82^{\circ}\).
The central angle for \(\widehat{HK}\) is \(90 + 82=172^{\circ}\).

Answer:

\(172\)