Question

given:
el⊥eh.
ex⊥ez.
m∠xeh = 60°.
enter the measures and reasons to justify each step needed
to calculate m∠lez.
m∠lez=
diagram notes:

Explanation:

Step1: Use the property of perpendicular lines

Since \(EL\perp EH\) and \(EX\perp EZ\), \(\angle LEX+\angle XEH = 90^{\circ}\) and \(\angle ZEH+\angle XEH=90^{\circ}\). Also, the sum of angles around a point \(E\) for the right - angle - related angles: \(\angle LEZ=\angle LEX + 90^{\circ}\) (because \(EX\perp EZ\) means \(\angle XEZ = 90^{\circ}\)).
First, find \(\angle LEX\). Given \(m\angle XEH = 60^{\circ}\) and \(\angle LEX+\angle XEH=90^{\circ}\) (complementary angles as \(EL\perp EH\)), then \(\angle LEX=90^{\circ}-m\angle XEH\).
Substitute \(m\angle XEH = 60^{\circ}\) into the formula: \(\angle LEX=90 - 60=30^{\circ}\).

Step2: Calculate \(\angle LEZ\)

Since \(\angle LEZ=\angle LEX+\angle XEZ\) and \(\angle XEZ = 90^{\circ}\) (because \(EX\perp EZ\)).
Substitute \(\angle LEX = 30^{\circ}\) and \(\angle XEZ=90^{\circ}\) into the formula: \(m\angle LEZ=30 + 90\).

Answer:

\(m\angle LEZ = 120^{\circ}\)