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: $\text{m}\angle T=45^{\circ}$

Step-by-step 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,

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

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

Hence, $\text{m}\angle T=45^{\circ}$