Question

hi and jk intersect at point o. m∠koh = 110°. colleen was asked to find the measure of ∠x and explain her reasoning. fill in the blanks in colleens solution. since ∠koh and ∠iok form a linear pair, m∠iok = 70°. ∠x and ∠koh form a linear pair, so m∠x =

Explanation:

Step1: Recall linear - pair property

A linear pair of angles sums to 180°. Given \(m\angle KOH = 110^{\circ}\), and \(\angle KOH\) and \(\angle IOK\) are a linear pair. So \(m\angle IOK=180 - m\angle KOH\).
\[m\angle IOK = 180-110=70^{\circ}\]

Step2: Identify linear - pair for \(\angle x\)

\(\angle x\) and \(\angle KOH\) form a linear pair. Since the sum of angles in a linear pair is 180°, we have \(m\angle x=180 - m\angle KOH\).
\[m\angle x=180 - 110 = 70^{\circ}\]

Answer:

70