Question

In ∆TMZ, the measure of angle M is 6° more than twice the measure of angle T, and the measure of angle Z is 50° less than five times the measure of angle T.

Answer 1

Answer:

m<T = $28^{o}$, m<M = $62^{o}$ and m<Z = $90^{o}$

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 = $180^{o}$

T + (2T + 6°) + (5T - 50°) = $180^{o}$

8T -$44^{o}$ = $180^{o}$

8T = $180^{o}$ + $44^{o}$

    = $224^{o}$

T = $\frac{224^{o} }{8}$

   = $28^{o}$

Therefore,

i. m<T = $28^{o}$

ii. m<M = 2T + 6°

        = 2 x $28^{o}$ + 6°

        = $62^{o}$

m<M = $62^{o}$

iii. m<Z = 5T - 50°

            = 5 x $28^{o}$ - 50°

            = $140^{o}$ - 50°

            = $90^{o}$

m<Z = $90^{o}$