Question

Find the value of s in rhombus UVWX.WV3s-41°S+61°ХU

Answer 1

In the rhombus, every 2 opposite angles are equal in measures

In the rhombus UVWX

Since < X and < V are opposite angles, then they are equal in measures

Since < x = (s + 61) degrees

Since < V = (3s - 41) degrees

Equate them

$3s-41=s+61$

Add 41 to both sides

$\begin{gathered} 3s-41+41=s+61+41 \\ 3s=s+102 \end{gathered}$

Subtract s from both sides

$\begin{gathered} 3s-s=s-s+102 \\ 2s=102 \end{gathered}$

Divide both sides by 2 to find s

$\begin{gathered} \frac{2s}{2}=\frac{102}{2} \\ s=51 \end{gathered}$

The value of s is 51