Math Problem Statement

You are asked to fabricate the following shape. What is the size of angle D in the diagram? Angles A, B, and C are 115°, 136°, and 38°, respectively.

Solution

The problem provides three angles of a quadrilateral (A, B, C) and asks for the fourth angle (D). Specifically, we know:

  • A=115\angle A = 115^\circ
  • B=136\angle B = 136^\circ
  • C=38\angle C = 38^\circ

In any quadrilateral, the sum of all interior angles is always 360 degrees. Using this fact, we can determine the value of D\angle D by summing the known angles and subtracting from 360°.

Here's the calculation:

D=360(A+B+C)\angle D = 360^\circ - (\angle A + \angle B + \angle C)

Substitute the given values:

D=360(115+136+38)\angle D = 360^\circ - (115^\circ + 136^\circ + 38^\circ)

D=360289=71\angle D = 360^\circ - 289^\circ = 71^\circ

Thus, D=71\angle D = 71^\circ.

Would you like more details, or do you have any questions?

Follow-up Questions:

  1. What is the formula to find the sum of angles in a polygon?
  2. How does the sum of angles change for different polygons (triangle, pentagon, etc.)?
  3. Why do quadrilaterals always have a total of 360°?
  4. Can you use this method for irregular quadrilaterals as well?
  5. How would the problem change if one of the angles were unknown instead of three?

Tip:

Remember, the sum of interior angles of any polygon can be calculated using the formula (n2)×180(n-2) \times 180^\circ, where nn is the number of sides of the polygon.

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Angle Sum of Polygons

Formulas

Sum of interior angles in a quadrilateral = 360°

Theorems

Interior Angle Sum Theorem

Suitable Grade Level

Grades 6-8