Question

given △rws≅△tuv, find the values (a) x (b) y. r (4x - 21)° 15 20 s w 25 u 25 3y + 7 t v

Explanation:

Step1: Identify corresponding sides and angles of congruent triangles

Since $\triangle RWS\cong\triangle TUV$, corresponding sides and angles are equal. $\angle R$ corresponds to $\angle T$, and side $WS$ corresponds to side $UV$, side $RS$ corresponds to side $TV$.

Step2: Set up equations for $x$

$\angle R=\angle T$, so $8x - 21=29$.
Add 21 to both sides: $8x=29 + 21$, $8x=50$.
Divide both sides by 8: $x=\frac{50}{8}=\frac{25}{4}=6.25$.

Step3: Set up equations for $y$

$WS = UV$, so $y=25$.

Answer:

$x = 6.25$, $y = 25$