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3 years ago

7

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 t

imes the measure of angle T.

1 answer:

uysha [10]3 years ago

7 0

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 = $90^{o}$

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