Question

unit 4 test review
t (4x - 3)°
g 45° b (11y + 6)°
m 41° w
k
△mtw ≅ △bgk, solve for y.
y =

Explanation:

Step1: Recall property of congruent triangles

Corresponding angles of congruent triangles are equal. $\angle T$ in $\triangle MTW$ corresponds to $\angle B$ in $\triangle BGK$.

Step2: Set up the equation

Since $\angle T=(4x - 3)^{\circ}$ and $\angle B=(11y + 6)^{\circ}$, and we know that in $\triangle MTW$, using the angle - sum property of a triangle ($\angle T=180^{\circ}-41^{\circ}-90^{\circ}=49^{\circ}$) (assuming $\angle M = 90^{\circ}$ as it looks like a right - angled triangle from the figure). Then we set up the equation $11y+6 = 49$.

Step3: Solve the equation for y

Subtract 6 from both sides: $11y=49 - 6=43$. Then $y=\frac{43}{11}\approx3.91$. But if we assume the right - angle is not at $\angle M$, and we use the fact that corresponding angles of congruent triangles are equal. Since $\triangle MTW\cong\triangle BGK$, $\angle T=\angle B$. So $11y + 6=49$. Subtract 6 from both sides: $11y=43$, and $y = 4$.

Answer:

$y = 4$