Question

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

Answer 1

The set of values are described below:

`v = 25\,cm`,
`w = 25^(\circ)`,
`x = 25^(\circ)`,
`y = 65^(\circ)` and
`z = 10\,cm`.

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`.