Question

what is ( mangle phj )?
( 100^{circ} )
( 120^{circ} )
( 140^{circ} )
( 160^{circ} )

Explanation:

Step1: Calculate the angle adjacent to \(140^{\circ}\)

Since the sum of angles on a straight line is \(180^{\circ}\), the angle adjacent to \(140^{\circ}\) is \(180^{\circ}- 140^{\circ}=40^{\circ}\)

Step2: Calculate \(m\angle PHJ\)

We know that the sum of angles around a point is \(360^{\circ}\), but we can also use the fact that \(m\angle PHJ = 180^{\circ}-(40^{\circ}-20^{\circ})\) (using the straight - line angle property). Another way is to note that \(m\angle PHJ=180^{\circ}- 20^{\circ}- 40^{\circ}\). First, \(180^{\circ}-20^{\circ}=160^{\circ}\), then \(160^{\circ}-40^{\circ}=120^{\circ}\)

Answer:

\(120^{\circ}\)