Question

triangle nop is formed by connecting the midpoints of the side of triangle klm. the measures of the interior are shown. find the measure of ∠lno. figures not necessarily drawn to scale.
answer attempt 1 out of 2
m∠lno = ° submit answer

Explanation:

Step1: Find the measure of ∠KML

Use the triangle - angle sum theorem (\(\angle K+\angle L+\angle M = 180^{\circ}\)).
Given \(\angle K = 82^{\circ}\), \(\angle L=48^{\circ}\).
So, \(\angle M=180^{\circ}-(82^{\circ} + 48^{\circ})=180^{\circ}-130^{\circ}=50^{\circ}\).

Step2: Use the mid - segment properties

Since \(N\), \(O\), \(P\) are mid - points of the sides of \(\triangle KLM\), \(PN\parallel LM\) and \(ON\parallel KM\) (mid - segment theorem: the segment connecting the mid - points of two sides of a triangle is parallel to the third side).
Quadrilateral \(PNOM\) is a parallelogram (a quadrilateral with both pairs of opposite sides parallel). So, \(\angle LNO=\angle K\) (corresponding angles of parallel lines).

Answer:

\(82\)