Math Problem Statement

Given the rhombus with m <CAB = 35 º, find m <CDA.

Solution

In a rhombus, opposite angles are equal, and adjacent angles are supplementary (i.e., they add up to 180º). Here's the step-by-step reasoning:

  1. Given information: mCAB=35m \angle CAB = 35^\circ.
  2. Opposite angles: In a rhombus, opposite angles are equal, so mDAB=mCAB=35m \angle DAB = m \angle CAB = 35^\circ.
  3. Adjacent angles: Adjacent angles in a rhombus are supplementary, so: mDAB+mCDA=180m \angle DAB + m \angle CDA = 180^\circ Substituting mDAB=35m \angle DAB = 35^\circ: 35+mCDA=18035^\circ + m \angle CDA = 180^\circ Solving for mCDAm \angle CDA: mCDA=18035=145m \angle CDA = 180^\circ - 35^\circ = 145^\circ

Thus, mCDA=145m \angle CDA = 145^\circ.

Would you like a further explanation or have any questions? Here are a few related questions you might find interesting:

  1. How do you calculate the angles in a parallelogram?
  2. What are the properties of the diagonals of a rhombus?
  3. How can you prove that opposite angles of a rhombus are equal?
  4. How do you calculate the area of a rhombus given its side length and one of the angles?
  5. What is the relationship between the diagonals and angles in a rhombus?

Tip: Always remember that the sum of the interior angles of any quadrilateral is 360º, which helps in angle-related problems!

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Math Problem Analysis

Mathematical Concepts

Geometry
Rhombus Properties
Angles of Quadrilaterals

Formulas

Adjacent angles in a rhombus are supplementary (sum to 180º)

Theorems

Opposite angles of a rhombus are equal
Adjacent angles in a rhombus are supplementary

Suitable Grade Level

Grades 7-10