Math Problem Statement

answer

Find the value of angle c in the given quadrilateral with angles 65°, 127°, and 140° provided.

Solution

This diagram is of a quadrilateral where the sum of the interior angles is always 360360^\circ. Here's how we calculate cc:

Step-by-step solution:

  1. The given angles in the quadrilateral are:

    • 6565^\circ
    • 127127^\circ
    • 140140^\circ
    • Angle cc (to be found).
  2. Use the sum of the interior angles of a quadrilateral: 65+127+140+c=36065^\circ + 127^\circ + 140^\circ + c = 360^\circ

  3. Add the known angles: 65+127+140=33265 + 127 + 140 = 332^\circ

  4. Solve for cc: c=360332=28c = 360^\circ - 332^\circ = 28^\circ

Final Answer:

c=28c = 28^\circ

Would you like a detailed explanation of any step?

Related Questions:

  1. What is the sum of angles in a pentagon, and how is it calculated?
  2. If one angle of a quadrilateral is 9090^\circ, how does it affect the other angles?
  3. Can a quadrilateral have all angles obtuse? Why or why not?
  4. What is the difference between a convex and concave quadrilateral in terms of angles?
  5. How do you calculate angles when a quadrilateral is inscribed in a circle?

Tip:

When solving angle problems, always check whether the shape is regular (like a rectangle or square) or irregular, as this influences angle relationships.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in a Quadrilateral

Formulas

Sum of interior angles of a quadrilateral: 360°

Theorems

Angle Sum Property of Quadrilaterals

Suitable Grade Level

Grades 6-8