Question

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

Explanation:

Step1: Recall angle classifications

• A right angle is exactly \(90^\circ\).
• An acute angle is less than \(90^\circ\) (and greater than \(0^\circ\)).
• An obtuse angle is greater than \(90^\circ\) (and less than \(180^\circ\)).

Step2: Classify \(\angle A\)

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

Step3: Classify \(\angle B\)

\(\angle B = 75^\circ\), and \(75^\circ< 90^\circ\), 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 \(\angle A\) and \(\angle D\), select "Right"; for \(\angle B\), select "Acute"; for \(\angle C\), select "Obtuse".)