Question

triangle opq is formed by connecting the midpoints of the side of triangle lmn. the measures of the interior angles of triangle lmn are shown. find the measure of ∠mpo. figures not necessarily drawn to scale. answer m∠mpo =

Explanation:

Step1: Use the mid - segment theorem

Since \(OP\) is a mid - segment of \(\triangle LMN\) (connecting midpoints of two sides), \(OP\parallel LN\).

Step2: Use the property of parallel lines and transversal

When \(OP\parallel LN\) and \(MP\) is a transversal, \(\angle MPO\) and \(\angle LNP\) are corresponding angles.
Given \(\angle LNP = 34^{\circ}\)

Answer:

\(34^{\circ}\)