Question

what is m∠phj? 100° 120° 140° 160°

Explanation:

Step1: Recall angle - sum property at a point

The sum of angles around a point is 360°.

Step2: Let \(m\angle PHJ=x\)

We know that \(140^{\circ}+20^{\circ}+x = 180^{\circ}\) (since the non - overlapping angles around point \(H\) on one side of a straight - line formed by the rays contribute to a straight - angle or 180°).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180^{\circ}-(140^{\circ} + 20^{\circ})\\ x&=180^{\circ}-160^{\circ}\\ x& = 20^{\circ} \end{align*}$$

\]
But this is wrong. Let's consider the correct approach. The angles around point \(H\) are related such that \(m\angle MHL=140^{\circ}\), \(m\angle LHK\) is part of the angles around \(H\), and \(m\angle KHP = 20^{\circ}\). We want \(m\angle PHJ\).
We know that the sum of angles around point \(H\) is 360°. Also, we can use the fact that \(m\angle MHL\) and \(m\angle LHJ\) are supplementary (form a straight - line), so \(m\angle LHJ=180^{\circ}-140^{\circ}=40^{\circ}\).
Then \(m\angle PHJ=m\angle LHJ + m\angle KHP\).
\[

$$\begin{align*} m\angle PHJ&=(180 - 140)^{\circ}+20^{\circ}\\ &=40^{\circ}+20^{\circ}\\ &=100^{\circ} \end{align*}$$

\]

Answer:

100°