Question

In the Rhombus, m<3=80. Find m<2

160
80
50
40

Answer 1

m<2 = m<1 = 50°

Step-by-step explanation:

In a Rhombus, Diagonals intersect at 90° as well bisect angles.

Therefore, in a triangle formed by <1, 90° at the diagonal intersection and angle bisection of <3 = 40°.

m<1 = m<2 = 50°

Answer 2

Answer: C. 50

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Step-by-step explanation:

The diagonal cuts the rhombus into two congruent isosceles triangles. We know they are isosceles because the non-diagonal sides are equal in length (since all four sides of a rhombus are the same length).

Let x be the measure of angle 1. This is one base angle. The other base angle is also x as well. The third angle of the bottom triangle is angle 3, which is given to us at 80 degrees. For any triangle the three angles always add to 180.

x+x+80 = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

Angle 1 is therefore 50 degrees.

Angle 2 is also 50 degrees because angles 1 and 2 are congruent alternate interior angles. Any rhombus is a parallelogram (but not the other way around) so the top and bottom lines of the rhombus are parallel, allowing the alternate interior angles to be congruent.