Question

drag and drop the correct angle measures onto the diagram:
drag & drop the answer
60°
65°
120°
115°
note: use ctrl+d to drag the option via keyboard
(diagram with two parallel horizontal lines, two transversal lines, one transversal has a 120° angle marked, the other has a 65° angle marked, and empty boxes to drag and drop angle measures: 60°, 65°, 120°, 115°)

Explanation:

Step1: Analyze Vertical Angles

Vertical angles are equal. For the \( 120^\circ \) angle, its vertical angle is also \( 120^\circ \). For the \( 65^\circ \) angle, its vertical angle is \( 65^\circ \).

Step2: Analyze Supplementary Angles

Supplementary angles sum to \( 180^\circ \). For \( 120^\circ \), the supplementary angle is \( 180 - 120 = 60^\circ \). For \( 65^\circ \), the supplementary angle is \( 180 - 65 = 115^\circ \).

Step3: Apply Corresponding Angles (Parallel Lines)

Corresponding angles are equal. So angles corresponding to \( 60^\circ \) are \( 60^\circ \), to \( 65^\circ \) are \( 65^\circ \), to \( 115^\circ \) are \( 115^\circ \), and to \( 120^\circ \) are \( 120^\circ \).

Answer:

Using vertical angles, supplementary angles, and corresponding angles (for parallel lines):

• Angles equal to \( 60^\circ \): from \( 180 - 120 \), and corresponding angles.
• Angles equal to \( 65^\circ \): vertical angles and corresponding angles.
• Angles equal to \( 115^\circ \): \( 180 - 65 \) and corresponding angles.
• Angles equal to \( 120^\circ \): vertical angles and corresponding angles.

So the angle measures to drag: \( 60^\circ \), \( 65^\circ \), \( 115^\circ \), \( 120^\circ \) (placed based on vertical, supplementary, and corresponding angle relationships).