Question

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Explanation:

Identify the given geometric elements

Using the Angle Relationships knowledge point
We are given a rectangular canvas with three straight lines drawn inside.

• One line is vertical, meeting a horizontal line at a right angle \(90^\circ\).
• A diagonal line intersects both the vertical and horizontal lines.
• The acute angle between the diagonal line and the vertical line is given as \(45^\circ\).

Determine the angle adjacent to the right angle

Using the Angle Relationships knowledge point
The vertical line and the horizontal line are perpendicular, forming a right angle of \(90^\circ\).
The angle between the diagonal line and the horizontal line in that same upper-right quadrant is:

$$ 90^\circ - 45^\circ = 45^\circ $$

Calculate the supplementary angle for \(x\)

Using the Supplementary Angles knowledge point
The diagonal line and the horizontal line intersect.
The angle \(x\) and the adjacent angle on the straight line are supplementary.
The angle vertically opposite to the \(45^\circ\) angle formed with the vertical line is also \(45^\circ\).
Since the horizontal line is straight, the angle \(x\) and the adjacent angle of \(45^\circ\) lie on a straight line:

$$ x + 45^\circ = 180^\circ $$

$$ x = 180^\circ - 45^\circ = 135^\circ $$

Answer:

What is the size of angle x? <blank>135</blank> degrees