Math Problem Statement
Find the measure of the three missing angles in the rhombus where one angle is 78°.
Solution
To solve for the missing angles , , and in the rhombus, we can use the following properties:
- All angles in a quadrilateral add up to 360°.
- Opposite angles in a rhombus are equal.
- Adjacent angles in a rhombus are supplementary (add up to 180°).
From the image:
- One angle is given as at the bottom left.
- Let the opposite angle at the top right be , so (since opposite angles are equal).
- The adjacent angles and must each satisfy and because they are supplementary.
Thus:
Therefore, the three missing angles are:
Would you like more details on any of the steps? Here are five related questions to expand your understanding:
- What other properties of rhombuses can help in solving geometry problems?
- How would this solution change if the given angle was different, like 90° or 120°?
- How do the properties of parallelograms apply to rhombuses?
- What is the relationship between the diagonals of a rhombus and its angles?
- How do you derive the total sum of interior angles for any polygon?
Tip: Always remember that opposite angles of a rhombus are equal, and adjacent angles are supplementary. This simplifies the angle calculations significantly!
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Math Problem Analysis
Mathematical Concepts
Geometry
Properties of Rhombus
Quadrilaterals
Formulas
Sum of interior angles of a quadrilateral = 360°
Theorems
Opposite angles of a rhombus are equal
Adjacent angles in a rhombus are supplementary
Suitable Grade Level
Grades 7-9