Answer:
m<T = [tex]28^{o}[/tex], m<M = [tex]62^{o}[/tex] and m<Z = [tex]90^{o}[/tex]
Step-by-step explanation:
From the given ∆TMZ, let the measure angle T be represented by T.
So that,
m<M = 2T + 6°
m<Z = 5T - 50°
Sum of angles in a triangle = [tex]180^{o}[/tex]
T + (2T + 6°) + (5T - 50°) = [tex]180^{o}[/tex]
8T -[tex]44^{o}[/tex] = [tex]180^{o}[/tex]
8T = [tex]180^{o}[/tex] + [tex]44^{o}[/tex]
= [tex]224^{o}[/tex]
T = [tex]\frac{224^{o} }{8}[/tex]
= [tex]28^{o}[/tex]
Therefore,
i. m<T = [tex]28^{o}[/tex]
ii. m<M = 2T + 6°
= 2 x [tex]28^{o}[/tex] + 6°
= [tex]62^{o}[/tex]
m<M = [tex]62^{o}[/tex]
iii. m<Z = 5T - 50°
= 5 x [tex]28^{o}[/tex] - 50°
= [tex]140^{o}[/tex] - 50°
= [tex]90^{o}[/tex]
m<Z = [tex]90^{o}[/tex]
