Question

if ( hk = jk = 49 ) and ( mangle jik = 60^{circ} ), what is ( mangle hij )?

( mangle hij = square^{circ} )

Explanation:

Step1: Apply the Hypotenuse - Leg (HL) Congruence Theorem

Since \(HK = JK = 49\), \(IK\) is the common hypotenuse, and \(\angle H=\angle J = 90^{\circ}\), by the HL - Congruence Theorem, \(\triangle HIK\cong\triangle JIK\).

Step2: Use the property of congruent triangles

If \(\triangle HIK\cong\triangle JIK\), then \(\angle HIK=\angle JIK\).

Step3: Calculate \(m\angle HIJ\)

Given \(m\angle JIK = 60^{\circ}\), and \(m\angle HIJ=m\angle HIK + m\angle JIK\). Since \(\angle HIK=\angle JIK = 60^{\circ}\), then \(m\angle HIJ=60^{\circ}+ 60^{\circ}\).

Answer:

\(120\)