Math Problem Statement

Вычисли остальные углы параллелограмма, если угол C равен 44°.

Solution

To solve the problem and find the remaining angles of the parallelogram, we will use the properties of a parallelogram:

  1. Opposite angles are equal.
  2. Adjacent angles are supplementary (sum up to 180180^\circ).

Given:

  • C=44\angle C = 44^\circ

Step-by-Step Solution:

  1. Since opposite angles are equal, we know: A=C=44\angle A = \angle C = 44^\circ

  2. The adjacent angles are supplementary: C+D=180\angle C + \angle D = 180^\circ Substituting C=44\angle C = 44^\circ: 44+D=18044^\circ + \angle D = 180^\circ Solving for D\angle D: D=18044=136\angle D = 180^\circ - 44^\circ = 136^\circ

  3. Since opposite angles are equal, we know: B=D=136\angle B = \angle D = 136^\circ

Final Answer:

  • B=136\angle B = 136^\circ
  • A=44\angle A = 44^\circ
  • D=136\angle D = 136^\circ

Let me know if you need further clarification!


Related Questions:

  1. What are the properties of a parallelogram?
  2. How do you calculate adjacent angles in any quadrilateral?
  3. What are the special cases of parallelograms, like rectangles or rhombuses?
  4. How do you prove that opposite angles are equal in a parallelogram?
  5. Can the interior angles of a parallelogram ever be all equal?

Tip:

Always remember that in a parallelogram, opposite angles are congruent, and consecutive (adjacent) angles are supplementary.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Parallelogram Properties
Angles

Formulas

Sum of adjacent angles in a parallelogram: ∠C + ∠D = 180°
Opposite angles in a parallelogram are equal: ∠A = ∠C, ∠B = ∠D

Theorems

Properties of a Parallelogram

Suitable Grade Level

Grades 6-8