Math Problem Statement

You are asked to fabricate the following shape where the two known angles, S and T, are 55°. Calculate the other two angles.

Solution

The problem shows a quadrilateral RSTURSTU, with two known angles: S=55\angle S = 55^\circ and T=55\angle T = 55^\circ. We need to calculate the other two angles: R\angle R and U\angle U.

Since RSTURSTU is a parallelogram (as inferred from the shape), we can apply the following properties of parallelograms:

  1. Opposite angles are equal: R=U\angle R = \angle U.
  2. Adjacent angles are supplementary, meaning their sum is 180180^\circ.

Given:

  • S=55\angle S = 55^\circ and T=55\angle T = 55^\circ,
  • The adjacent angles R\angle R and U\angle U must satisfy R+S=180\angle R + \angle S = 180^\circ.

Thus: R+55=180\angle R + 55^\circ = 180^\circ R=18055=125\angle R = 180^\circ - 55^\circ = 125^\circ

Therefore, both R\angle R and U\angle U are 125125^\circ.

Summary:

  • S=55\angle S = 55^\circ
  • T=55\angle T = 55^\circ
  • R=125\angle R = 125^\circ
  • U=125\angle U = 125^\circ

Let me know if you would like further clarification or have additional questions!

Here are 5 related questions:

  1. How do you calculate the interior angles of any parallelogram?
  2. What are the properties of quadrilaterals like rectangles or rhombuses?
  3. What is the sum of the interior angles of any quadrilateral?
  4. Can a parallelogram have four equal angles? If so, what shape would it be?
  5. How would you calculate the angles if only one angle was given?

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

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Parallelograms

Formulas

Opposite angles in a parallelogram are equal.
Adjacent angles in a parallelogram are supplementary (sum to 180°).

Theorems

Parallelogram Angle Theorem: Opposite angles are equal.
Supplementary Angles Theorem: Adjacent angles sum to 180°.

Suitable Grade Level

Grades 6-8