Question

in the figure below, \\( \angle kol \\) and \\( \angle lom \\) are adjacent angles. the figure is not necessarily drawn to scale. which of the following must be true?
hint: trust the notation!
a pair of adjacent angles
a \\( m \angle kol + m \angle lom = 90 ^ { \circ } \\)
b \\( m \angle kol + m \angle lom = 180 ^ { \circ } \\)
c \\( m \angle kom = m \angle kol + m \angle lom \\)

Explanation:

Step1: Recall the definition of adjacent angles

Adjacent angles are two angles that share a common vertex and a common side, and their non - common sides form a new angle.

Step2: Analyze the sum of adjacent angles

For adjacent angles \(\angle KOL\) and \(\angle LOM\), the measure of the angle formed by their non - common sides (\(\angle KOM\)) is the sum of the measures of \(\angle KOL\) and \(\angle LOM\). That is \(m\angle KOM=m\angle KOL + m\angle LOM\).
Options A and B assume specific angle sums (\(90^{\circ}\) and \(180^{\circ}\)) which are not given in the problem. There is no information to suggest that \(\angle KOM\) is a right angle (\(90^{\circ}\)) or a straight angle (\(180^{\circ}\)).

Answer:

C. \(m\angle KOM=m\angle KOL + m\angle LOM\)