Question

In ΔSTU, \text{m}\angle S = (2x+10)^{\circ}m∠S=(2x+10) ∘ , \text{m}\angle T = (3x-9)^{\circ}m∠T=(3x−9) ∘ , and \text{m}\angle U = (6x-19)^{\circ}m∠U=(6x−19) ∘ . Find \text{m}\angle T.M∠T.

Answer 1

Answer:
`\text{m}\angle T=45^(\circ)`

Explanation:

Given: In ΔSTU,
`\text{m}\angle S = (2x+10)^(\circ)` ,
`\text{m}\angle T = (3x-9)^(\circ)`,
`\text{m}\angle U = (6x-19)^(\circ)`

To find:
`\text{m}\angle T`.

We know that the sum of all the angles of a triangle is
`180^(\circ)`.

In ΔSTU,

`\text{m}\angle S+\text{m}\angle T+\text{m}\angle U=180^(\circ)\\\\ 2x+10+3x-9+6x-19=180\\\\ 11x-18=180\\\\11x =180+18\\\\11x=198\\\\x=(198)/(11)\\\\ x=18`

`\text{m}\angle T = (3(18)-9)^(\circ)\\\\=(54-9)^(\circ)\\\\= 45^(\circ)`

Hence,
`\text{m}\angle T=45^(\circ)`