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In the rhombus m∠1=160°
. What are m∠2
and m∠3
? The diagram is not drawn to scale.
A rhombus with a diagonal drawn horizontally is shown. The angle at the top vertex is labeled 1. The angle at the bottom vertex is labeled 3. The angle that the diagonal forms with the lower right side of the rhombus is labeled 3.
(2 points)
Since a rhombus has opposite angles that are congruent, we know that m∠1 = m∠3.
So, if m∠1 is 160°, then m∠3 is also 160°.
Now, let's label m∠2.
Since a rhombus has opposite angles that are congruent, we can use the fact that the sum of the angles in a quadrilateral is 360°.
Since we know m∠1 and m∠3 are 160° each, we can find m∠2 by subtracting their sum from 360°:
m∠2 = 360° - (m∠1 + m∠3)
= 360° - (160° + 160°)
= 360° - 320°
= 40°
Therefore, m∠2 is 40°.