Question

drag and drop the correct angle measures onto the diagram.
drag & drop the answer
135°
45°
180°
65°
note: use ctrl+clicking the option on keyboard
(diagram with quadrilateral lomn, angle at o is 135°, and some sides marked as equal, with empty boxes for angle measures at l, m, n)

Explanation:

Step1: Identify the figure type

The figure \( LMNO \) has \( LM \parallel ON \) (arrows indicate parallel lines) and \( LO = MN \) (marked with single ticks), so it's an isosceles trapezoid. In an isosceles trapezoid, base angles are equal, and consecutive angles between bases are supplementary.

Step2: Analyze angle at \( L \) and \( O \)

\( \angle O = 135^\circ \), so \( \angle L \) (supplementary to \( \angle O \)): \( 180^\circ - 135^\circ = 45^\circ \).

Step3: Analyze angle at \( M \) and \( N \)

Since it's isosceles, \( \angle M=\angle L = 45^\circ \), and \( \angle N=\angle O = 135^\circ \).

Answer:

• \( \angle L \): \( 45^\circ \)
• \( \angle M \): \( 45^\circ \)
• \( \angle N \): \( 135^\circ \)