Answer: The angle measures in the given triangle are:
∠JPL = 92 degrees
∠JPM = 50 degrees
∠MLO = 38 degrees
Step-by-step explanation: To find the angle measures in the given triangle, we can use the properties of triangles and the fact that the incenter of a triangle is the point where the angle bisectors intersect.
Let's denote the angles of the triangle as follows:
∠MJP = angle at point J
∠MLO = angle at point L
∠JPL = angle at point P
Given:
m∠MJP = 38
m∠MLO = 54
Since the incenter (denoted as point P) is the point where the angle bisectors intersect, we can conclude that:
m∠JPL = m∠MJP + m∠MLO = 38 + 54 = 92
Therefore, the measure of angle JPL is 92 degrees.
Next, we know that the sum of the angles in a triangle is always 180 degrees. Thus, we can find the measure of the remaining angle, ∠JPM, by subtracting the measures of the known angles from 180:
∠JPM = 180 - ∠MJP - ∠JPL = 180 - 38 - 92 = 50 degrees
Finally, to find the measure of angle MLO, we can use the fact that the angles of a triangle add up to 180 degrees:
∠MLO = 180 - ∠JPL - ∠JPM = 180 - 92 - 50 = 38 degrees.
