Question

classify the four angles of the quadrilateral.
diagram of quadrilateral labeled a, b, c, d with angles: ∠a=90°, ∠b=75°, ∠c=105°, ∠d=90°
table with columns right, acute, obtuse and rows ∠a, ∠b, ∠c, ∠d

Explanation:

Step1: Recall angle classifications

• Right angle: \( 90^\circ \)
• Acute angle: \( 0^\circ < \text{angle} < 90^\circ \)
• Obtuse angle: \( 90^\circ < \text{angle} < 180^\circ \)

Step2: Classify \( \angle A \)

\( \angle A = 90^\circ \), so it is a right angle.

Step3: Classify \( \angle B \)

\( \angle B = 75^\circ \), and \( 0^\circ < 75^\circ < 90^\circ \), so it is an acute angle.

Step4: Classify \( \angle C \)

\( \angle C = 105^\circ \), and \( 90^\circ < 105^\circ < 180^\circ \), so it is an obtuse angle.

Step5: Classify \( \angle D \)

\( \angle D = 90^\circ \), so it is a right angle.

Answer:

• \( \angle A \): Right
• \( \angle B \): Acute
• \( \angle C \): Obtuse
• \( \angle D \): Right

(To fill the table: For \( \angle A \), mark "Right"; for \( \angle B \), mark "Acute"; for \( \angle C \), mark "Obtuse"; for \( \angle D \), mark "Right".)