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

m<T =
`28^(o)`, m<M =
`62^(o)` and m<Z =
`90^(o)`

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 =
`(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)`