Question

what is m∠wxz?
m∠wxz = \square°

Explanation:

Step1: Recall angle sum on a straight line

Angles around a point on a straight line sum to \(180^\circ\)? No, wait, the sum of angles on a straight line (linear pair) is \(180^\circ\), but here we have three angles at point \(X\) forming a straight line? Wait, actually, the sum of angles around a point on a straight line (the total angle on a straight line is \(180^\circ\))? Wait, no, the three angles at \(X\): \(\angle WXY = 40^\circ\), \(\angle YXZ = 115^\circ\)? Wait, no, wait the diagram: \(WX\) is a straight line? Wait, no, \(WX\), \(XY\), and \(XZ\) meet at \(X\), and the sum of angles around a point on a straight line? Wait, actually, the sum of angles on a straight line is \(180^\circ\), but here we have three angles: \(\angle WXY = 40^\circ\), \(\angle YXZ = 115^\circ\)? No, wait, the angle between \(WX\) and \(XY\) is \(40^\circ\), between \(XY\) and \(XZ\) is \(115^\circ\)? Wait, no, that can't be. Wait, actually, the sum of angles around point \(X\) on a straight line (the total angle should be \(180^\circ\))? Wait, no, I think I made a mistake. Wait, the three angles at \(X\): \(\angle WXZ\) is what we need, \(\angle WXY = 40^\circ\), and \(\angle YXZ = 115^\circ\)? No, that can't be, because \(40 + 115 = 155\), and \(180 - 155 = 25\), which is wrong. Wait, no, maybe the angles are \(\angle WXY = 40^\circ\), \(\angle YXZ = 115^\circ\), and we need \(\angle WXZ\). Wait, no, actually, the sum of angles on a straight line is \(180^\circ\), but here, the three angles: \(\angle WXY\), \(\angle YXZ\), and wait, no, maybe the angle between \(WX\) and \(XZ\) is \(\angle WXZ\), and the other two angles are \(40^\circ\) and \(115^\circ\), but that can't be. Wait, no, the correct approach: the sum of angles around a point on a straight line (the total angle is \(180^\circ\))? Wait, no, I think the correct way is: the sum of angles on a straight line is \(180^\circ\), so \(\angle WXZ + 40^\circ + 115^\circ = 180^\circ\)? No, that would be \(180 - 40 - 115 = 25\), which is wrong. Wait, no, I must have misread the diagram. Wait, maybe the angle between \(WX\) and \(XY\) is \(40^\circ\), between \(XY\) and \(XZ\) is \(115^\circ\), but actually, the angle we need is \(\angle WXZ\), which is \(\angle WXY + \angle YXZ\)? Wait, \(40 + 115 = 155\), no. Wait, no, that's not right. Wait, maybe the sum of angles on a straight line is \(180^\circ\), so the angle adjacent to \(115^\circ\) is \(180 - 115 = 65^\circ\), then \(\angle WXZ = 40 + 65 = 105^\circ\). Ah, that makes sense. So step by step:

Step1: Find the supplementary angle to \(115^\circ\)

The angle adjacent to \(115^\circ\) (forming a linear pair) is \(180^\circ - 115^\circ = 65^\circ\).

Step2: Add the two angles to get \(\angle WXZ\)

Now, \(\angle WXZ\) is the sum of \(40^\circ\) and \(65^\circ\), so \(40 + 65 = 105^\circ\).

Answer:

105