Bisection is a process that produces two equal parts of angles or lines. Thus applying the bisection principle, the measure of angle lmn = [tex]168^{o}[/tex]
This question deals with sub-bisection of angles. Bisection is the method required to divide a given angle or line into two equal parts.
From the given question: m<rmp = [tex]21^{o}[/tex] (given)
But,
m<qmp = m<rmp + m<qmr = 2 x m<rmp (addition property of bisected angles)
= 2 x [tex]21^{o}[/tex]
m<qmp = [tex]42^{o}[/tex]
Also,
m<lmp = m<lmq + m<qmp = 2 x m<qmp (addition property of bisected angles)
= 2 x [tex]42^{o}[/tex]
m<lmp = [tex]84^{o}[/tex]
Then,
m<lmn = m<lmp + m<pmn = 2 x m<lmp (addition property of bisected angles)
= 2 x [tex]84^{o}[/tex]
m<lmn = [tex]168^{o}[/tex]
Thus, the measure of angle lmn is [tex]168^{o}[/tex].
A simple sketch is attached to the answer for more clarifications.
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