Question

use the diagram below to answer the questions.
find m∠krf.
label optional

Explanation:

Step1: Identify supplementary angles

The angle of \(147^\circ\) and \((-21b)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\). Wait, actually, looking at the diagram, \(\angle KRF\) and the \(147^\circ\) angle—wait, no, first, the angle labeled \((-21b)^\circ\) and \(147^\circ\) are adjacent and form a linear pair? Wait, no, maybe vertical angles or linear pair. Wait, actually, the angle we need, \(\angle KRF\), and the \(147^\circ\) angle—wait, no, let's correct. The angle of \(147^\circ\) and the angle adjacent to it (forming a linear pair) should add to \(180^\circ\). Wait, but maybe the angle \((-21b)^\circ\) is equal to the angle opposite? No, wait, the problem is to find \(m\angle KRF\). Wait, maybe the \(147^\circ\) and \(\angle KRF\) are supplementary? Wait, no, let's see: the two angles \(147^\circ\) and \((-21b)^\circ\) – wait, no, maybe the angle we need is supplementary to \(147^\circ\). Wait, linear pair: two angles on a straight line add to \(180^\circ\). So if one angle is \(147^\circ\), the adjacent angle (linear pair) is \(180 - 147 = 33^\circ\). Wait, maybe \(\angle KRF\) is that angle. Wait, let's check: \(180 - 147 = 33\). So \(m\angle KRF = 33^\circ\).

Step2: Calculate the measure

Using the linear pair property (sum of angles on a straight line is \(180^\circ\)):
\(m\angle KRF + 147^\circ = 180^\circ\)
Subtract \(147^\circ\) from both sides:
\(m\angle KRF = 180^\circ - 147^\circ = 33^\circ\)

Answer:

\(33^\circ\)