Question

what is m∠hjk? m∠hjk=□° submit

Explanation:

Step1: Use Hypotenuse - Leg Congruence

Since \(HI = HK = 92\) (given) and \(HJ\) is the common hypotenuse for right - triangles \(\triangle HIJ\) and \(\triangle HKJ\). By the Hypotenuse - Leg (HL) congruence criterion for right - triangles, \(\triangle HIJ\cong\triangle HKJ\).

Step2: Use Congruent - Triangle Properties

Because \(\triangle HIJ\cong\triangle HKJ\), the corresponding angles are equal. So, \(\angle IJH=\angle KJH\).

Step3: Calculate \(\angle HJK\)

We know that \(\angle IJK = 90^{\circ}\) (since \(\angle HIJ = 90^{\circ}\) and \(\angle HKJ = 90^{\circ}\) and the sum of angles around a point related to the right - angles). Given \(\angle IJH = 49^{\circ}\), and \(\angle HJK=\angle IJK-\angle IJH\).

$$m\angle HJK=90^{\circ}- 49^{\circ}$$

Answer:

\(41\)