Question

m∠jmk = ____ m∠hjl = ____
m∠jkh = ____ m∠lhk = ____
m∠hlk = ____ m∠jlk = ____

Explanation:

Step1: Identify rectangle properties

In rectangle \(HJLK\), diagonals are equal and bisect each other, so \(HM=ML=JM=MK\). Thus, \(\triangle JMK\) is isosceles, and \(\angle JMK\) is vertical to the given \(120^\circ\) angle.
\(m\angle JMK = 120^\circ\)

Step2: Calculate \(\angle JKH\)

In \(\triangle JMK\), base angles are equal. Sum of angles in a triangle is \(180^\circ\).
\(m\angle JKH = \frac{180^\circ - 120^\circ}{2} = 30^\circ\)

Step3: Calculate \(\angle HLK\)

\(\angle HLK = \angle JKH\) (alternate interior angles for parallel \(HJ\) and \(LK\), transversal \(HK\)), so \(m\angle HLK = 30^\circ\)

Step4: Calculate \(\angle HJL\)

\(\angle HJL = \angle JKH = 30^\circ\) (alternate interior angles for parallel \(HL\) and \(JK\), transversal \(HJ\))
\(m\angle HJL = 30^\circ\)

Step5: Calculate \(\angle LHK\)

\(\angle LHK = 90^\circ - m\angle HLK\) (since \(\angle HLK = 30^\circ\) and \(\angle HLK + \angle LHK = 90^\circ\) in right \(\triangle HLK\))
\(m\angle LHK = 90^\circ - 30^\circ = 60^\circ\)

Step6: Calculate \(\angle JLK\)

\(\angle JLK = 90^\circ - m\angle JKH\) (right angle of rectangle minus \(\angle JKH\))
\(m\angle JLK = 90^\circ - 30^\circ = 60^\circ\)

Answer:

\(m\angle JMK = 120^\circ\)
\(m\angle HJL = 30^\circ\)
\(m\angle JKH = 30^\circ\)
\(m\angle LHK = 60^\circ\)
\(m\angle HLK = 30^\circ\)
\(m\angle JLK = 60^\circ\)