Question

In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle.

Write and solve an equation to determine the measure of angle y.

Answer 1

The answer is "
`\angle y = 90^(\circ)`"

Explanation:

Please find the image file of the angle in the attachment.

Each line is 180° straight because the
`\angle x`-axis of the 40° and 50° angles is a straight line:

`= \angle x + 40^(\circ) + 50^(\circ) = 180^(\circ)`

Use this formula and isolate x.

`\angle x + 40^(\circ) + 50^(\circ) = 180^(\circ)\\\\ \angle x + 90^(\circ) = 180^(\circ) \\\\ \angle x = 180^(\circ) - 90^(\circ) \\\\ \angle x = 90^(\circ)\\\\`

Since the two are vertical angles, they have the same measurement. These have the same measurement. If
`\angle x = 90^(\circ)` and
`m \angle x = m \angle y`, then
`\angle y = 90^(\circ)`