Question

1. △abc≅△tuv. find the following side - length and angle measure.

a. find the m∠u
b. find the length of bc.

Explanation:

Step1: Use property of congruent triangles

Since $\triangle ABC\cong\triangle TUV$, corresponding sides are equal. So $BC = UV$. Set up the equation $6x + 2=6x - 1$ (this is wrong, should be $6x + 2=5x + 7$). Correctly, $6x+2 = 5x + 7$.

Step2: Solve for x

Subtract $5x$ from both sides: $6x-5x+2=5x - 5x+7$, which gives $x + 2=7$. Then subtract 2 from both sides: $x=7 - 2=5$.

Step3: Find length of BC

Substitute $x = 5$ into the expression for $BC$ which is $6x+2$. So $BC=6\times5+2=30 + 2=32$ cm.

Step4: Find measure of $\angle U$

Since $\triangle ABC\cong\triangle TUV$, corresponding angles are equal. $\angle B=\angle U$. Set up the equation $3y + 2=4y-18$.

Step5: Solve for y

Subtract $3y$ from both sides: $3y-3y + 2=4y-3y-18$, which gives $2=y - 18$. Add 18 to both sides: $y=2 + 18=20$.

Step6: Find measure of $\angle U$

Substitute $y = 20$ into the expression for $\angle U$ which is $4y-18$. So $\angle U=4\times20-18=80 - 18 = 62^{\circ}$.

Answer:

a. $m\angle U = 62^{\circ}$
b. $BC = 32$ cm