Question

use the similar figures at the right for the questions below.
find the scale factor of $delta rst$ to $delta uvw$.
find $m\angle v$.
solve for x.
blank 1:
blank 2:
blank 3:

Explanation:

Step1: Find scale factor (ΔRST→ΔUVW)

Scale factor = $\frac{\text{Side of } \Delta UVW}{\text{Side of } \Delta RST} = \frac{2}{4} = \frac{1}{2}$

Step2: Calculate $m\angle V$

First find $\angle S$ in $\Delta RST$:
$m\angle S = 180^\circ - 70^\circ - 62^\circ = 48^\circ$
Corresponding angles in similar triangles are equal, so $m\angle V = m\angle S = 48^\circ$

Step3: Solve for $x$

Use scale factor $\frac{1}{2}$:
$x = 7 \times \frac{1}{2} = 3.5$

Answer:

Blank 1: $\frac{1}{2}$
Blank 2: $48^\circ$
Blank 3: $3.5$