Question

Seatwork 5, solve for the values of v, w, x, y and z​

Answer 1

Answer:

The set of values are described below:

$v = 25\,cm$, $w = 25^{\circ}$, $x = 25^{\circ}$, $y = 65^{\circ}$ and $z = 10\,cm$.

Step-by-step explanation:

Since $\triangle JPO \cong \triangle SMR$, then $OJ \parallel RS$ and $OP \parallel RM$. By Alternate Internal Angles, we find that $\angle R \cong \angle O$. In addition, the sum of internal angles in triangles equals 180°. Then, we have the following system of linear equations:

$m\angle R + m\angle M + m\angle S = 180^{\circ}$ (1)

$m \angle O + m \angle P + m\angle J = 180^{\circ}$ (2)

$m\angle S = 65^{\circ}$ (3)

$m \angle M = m\angle P = 90^{\circ}$ (4)

The solution of this system is $m\angle R = 25^{\circ}$, $m \angle O = 25^{\circ}$ and $m \angle J = 65^{\circ}$.

Lastly, the remaining sides are found by definition of congruence

Segment RS

Since $\triangle JPO \cong \triangle SMR$, then $\overline {RS} \cong \overline {OJ}$. Hence, $RS = 25\,cm$

Segment JP

Since $\triangle JPO \cong \triangle SMR$, then $\overline{SM} \cong \overline {JP}$. Hence, $JP = 10\,cm$

The set of values are described below:

$v = 25\,cm$, $w = 25^{\circ}$, $x = 25^{\circ}$, $y = 65^{\circ}$ and $z = 10\,cm$.