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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.
Since opposite angles of a rhombus are congruent, we know that
m∠1 = m∠3 = 160°
Also, the sum of the angles in a triangle is 180°. Therefore, in triangle 3OD, we have:
m∠2 + m∠3 + 90° = 180°
m∠2 + 160° + 90° = 180°
m∠2 + 250° = 180°
m∠2 = 180° - 250°
m∠2 = -70°
Therefore,
m∠2 = -70°
m∠3 = 160°