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In the rhombus m∠1=160°
. What are m∠2
and m∠3
? The diagram is not drawn to scale.
In a rhombus, opposite angles are congruent. Therefore, m∠1 = m∠3. Since m∠1 = 160°, we can conclude that m∠3 = 160°.
The sum of the angles in any quadrilateral is 360°. Therefore, m∠1 + m∠2 + m∠3 + m∠4 = 360°. Since m∠1 = m∠3, let's substitute that:
160° + m∠2 + 160° + m∠4 = 360°
We can simplify the equation:
320° + m∠2 + m∠4 = 360°
Next, we subtract 320° from both sides:
m∠2 + m∠4 = 40°
In a rhombus, adjacent angles are supplementary. Therefore, m∠2 + m∠4 = 180°. We can use this information to set up another equation:
m∠2 + m∠4 = 180°
Now we have a system of equations:
m∠2 + m∠4 = 40°
m∠2 + m∠4 = 180°
Since both equations have m∠2 + m∠4, we can set them equal to each other:
40° = 180°
This is a contradiction, and there is no solution for m∠2 and m∠4 that satisfies both equations. Therefore, we cannot determine the values of m∠2 and m∠4 based on the given information.