Math Problem Statement

Classify the four angles of the quadrilateral based on their measurements (60°, 100°, 110°, and 90°) as right, acute, or obtuse.

Solution

The image shows a quadrilateral with labeled angles and a table to classify them as right, acute, or obtuse.

The angles in the quadrilateral are:

  • A=110\angle A = 110^\circ
  • B=60\angle B = 60^\circ
  • C=100\angle C = 100^\circ
  • D=90\angle D = 90^\circ

Classification of Angles:

  • Right angle: Measures exactly 9090^\circ.
  • Acute angle: Measures less than 9090^\circ.
  • Obtuse angle: Measures greater than 9090^\circ.

Using these definitions:

  • A=110\angle A = 110^\circObtuse
  • B=60\angle B = 60^\circAcute
  • C=100\angle C = 100^\circObtuse
  • D=90\angle D = 90^\circRight

So, the correct classification in the table would be:

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

Would you like any further clarification or additional details?

Follow-up Questions:

  1. How do you determine if a quadrilateral is convex or concave based on its angles?
  2. Can you name quadrilaterals that have exactly two obtuse angles?
  3. What is the sum of all interior angles in any quadrilateral, and why?
  4. How do you calculate missing angles in a quadrilateral if only three angles are given?
  5. Can you classify quadrilaterals based on their side lengths as well?

Tip: The sum of the interior angles of any quadrilateral is always 360360^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Angle Classification

Formulas

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Theorems

Angle Sum Theorem

Suitable Grade Level

Grades 6-8