Question

please help i’ve been stuck on this problem for some time

Answer 1

ANSWER

m∠T = 58°

EXPLANATION

If the two triangles are congruent, then their corresponding angles are congruent - and therefore their measures are the same:

$\begin{gathered} m\angle A=m\angle S \\ m\angle B=m\angle T \\ m\angle C=m\angle U \end{gathered}$

So the measure of angle T is the same as the measure of angle B. We have to find the value of x first.

The sum of the measures of the interior angles of any triangle is 180°. So we have for the second triangle:

$m\angle S+m\angle T+m\angle U=180\degree$

Remember that the measure of angle T is the same as angle B's. Replace with the expressions for the angle's measures:

$(4x+12)+(5x-27)+(3x-9)=180$

Add like terms:

$\begin{gathered} (4x+5x+3x)+(12-27-9)=180 \\ 12x-24=180 \end{gathered}$

Solve for x. Add 24 to both sides of the equation:

$\begin{gathered} 12x-24+24=180+24 \\ 12x=104 \end{gathered}$

And divide both sides by 12:

$\begin{gathered} \frac{12x}{12}=\frac{204}{12} \\ x=17 \end{gathered}$

Now we replace x = 17 into the expression for angle's T measure and solve:

$\begin{gathered} m\angle T=m\angle B=5x-27 \\ m\angle T=5\cdot17-27 \\ m\angle T=85-27 \\ m\angle T=58\degree \end{gathered}$