The measure of angle LON in triangle MNO is 35 degrees, as the triangles MNO and JKL are similar and corresponding angles are equal.
To find the measure of angle LON in triangle MNO, which is a triangle formed by connecting the midpoints of the sides of triangle JKL, we first note that the angles of a triangle add up to 180 degrees.
Given that the measures of angles in triangle JKL are 35 degrees, 91 degrees, and 54 degrees, we can deduce that triangle MNO is similar to triangle JKL, as the sides of MNO are parallel to the sides of JKL and MNO is thus formed by the midsegment theorem.
Since the triangles are similar, their corresponding angles are equal.
Angle L in triangle JKL corresponds to angle LON in triangle MNO, so the measure of angle LON is also 35 degrees.
The probable question may be:
Triangle MNO is formed by connecting the midpoints of the side of triangle JKL. The measures of the interior angles of triangle KL are shown. Find the measure of angle, LON. Figures not necessarily drawn to scale.
measure of angle L= 35 degree
measure of angle K= 91 degree
measure of angle J= 54 degree