Question

given: (overleftrightarrow{hi}) and (overleftrightarrow{jk}) intersect at point (o), (mangle koh = 110^{circ}). colleen was asked to find the measure of (angle x) and explain her reasoning. fill in the blanks in colleens solution. since (angle koh) and (angle iok) form a linear - pair, (mangle iok=square^{circ}). (angle x) and (square) form a linear pair, so (mangle x=square^{circ}).

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning their sum is 180°. Given \(m\angle KOH = 110^{\circ}\), and \(\angle KOH\) and \(\angle IOK\) form a linear pair. So \(m\angle IOK=180 - 110\).
\[m\angle IOK = 70^{\circ}\]

Step2: Identify another linear - pair

\(\angle x\) and \(\angle KOH\) form a linear pair. Since a linear pair of angles sums to 180°, and \(m\angle KOH = 110^{\circ}\), then \(m\angle x=180 - 110\).
\[m\angle x = 70^{\circ}\]

Answer:

• Since \(\angle KOH\) and \(\angle IOK\) form a linear pair, \(m\angle IOK = 70^{\circ}\).
• \(\angle x\) and \(\angle KOH\) form a linear pair, so \(m\angle x = 70^{\circ}\).