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 = . ∠x and ∠koh form a linear pair, so m∠x = 70°.

Explanation:

Step1: Recall linear - pair property

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

Step2: Identify another linear - pair

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

Answer:

The first blank: 70; The second blank: \(\angle KOH\)