In the rhombus pictured, m<1=140 ° . What are m<2 and the m<3? Please sure all work in order to receive full credit.

Answer 1

To solve for the measures of angles 2 and 3, let's first consider the properties of a rhombus.

A rhombus is a quadrilateral with all sides equal in length.
In a rhombus, opposite angles are congruent.

Given that angle 1 measures 140°, we can conclude that angle 3 is also 140° because they are opposite angles.

To find the measure of angle 2, we can use the fact that the sum of the interior angles of any quadrilateral is equal to 360°.

In this case, we know that angle 1 is 140° and angle 3 is 140°. Thus, the sum of angles 1, 2, 3, and 4 is equal to 360°. Since angle 4 is congruent to angle 2 (opposite angles in a rhombus), we can write the equation:

140° + 140° + angle 2 + angle 2 = 360°.

Simplifying the equation:

280° + 2(angle 2) = 360°.

Subtracting 280° from both sides:

2(angle 2) = 360° - 280°.
2(angle 2) = 80°.

Dividing both sides by 2 to isolate angle 2:

(angle 2) = 80° / 2.
(angle 2) = 40°.

Therefore, the measure of angle 2 is 40° and the measure of angle 3 is 140°.