Question

what is m∠phj? 100° 120° 140° 160°

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360°. Also, we know that \(\angle MHL = 140^{\circ}\) and \(\angle KHP=20^{\circ}\), and we want to find \(\angle PHJ\). Since \(\angle MHL+\angle LHJ + \angle JHP+\angle PHK=360^{\circ}\), and \(\angle MHL\) and \(\angle LHJ\) are a linear - pair, \(\angle LHJ = 180^{\circ}-\angle MHL\). First, note that \(\angle MHL\) and \(\angle LHJ\) are supplementary. \(\angle LHJ = 180 - 140=40^{\circ}\).

Step2: Calculate \(\angle PHJ\)

We know that the sum of angles around point \(H\) is 360°. But we can also use the fact that \(\angle PHJ=180^{\circ}-\angle KHP\). Substitute \(\angle KHP = 20^{\circ}\) into the formula. So, \(\angle PHJ=180 - 20=160^{\circ}\).

Answer:

160°