Question

1. solve for m∠t setup: x= m∠t =

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(6x - 6)+(7x + 1)+55=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(6x+7x)+(-6 + 1+55)=180$, which gives $13x+50 = 180$.

Step3: Solve for x

Subtract 50 from both sides: $13x=180 - 50=130$. Then divide both sides by 13: $x=\frac{130}{13}=10$.

Step4: Find the measure of angle T

Substitute $x = 10$ into the expression for $\angle T$. $m\angle T=(6x - 6)^{\circ}$. So, $m\angle T=(6\times10 - 6)^{\circ}=(60 - 6)^{\circ}=54^{\circ}$.

Answer:

setup: $(6x - 6)+(7x + 1)+55=180$
x = 10
$m\angle T=54^{\circ}$