in the rhombus angle 1=140. what are angle 2 and angle 3?
a. angle 2=140, angle 3=20
b. angle 2=40, angle 3=70
c. angle 2=40, angle 3=20
d. angle 2=140, angle 3=70
could be any of the choices, depending on the unseen and unexplained diagram.
To find the values of angle 2 and angle 3 in a rhombus when angle 1 is given, we need to understand the properties of rhombuses. In a rhombus, all four sides are equal in length, and opposite angles are equal in measure.
Since angle 1 is given as 140 degrees, we know that angle 1 is equal to angle 3 because they are opposite angles. Therefore, angle 3 is also 140 degrees.
To find the value of angle 2, we can use the fact that the sum of the measures of the angles in any quadrilateral is 360 degrees. Since a rhombus is a quadrilateral, we know that angle 1 + angle 2 + angle 3 + angle 4 = 360 degrees.
As we know angle 1 and angle 3 are both 140 degrees, we can substitute these values into the equation:
140 + angle 2 + 140 + angle 4 = 360
Simplifying the equation:
280 + angle 2 + angle 4 = 360
Now, since opposite angles in a rhombus are equal, angle 2 must be equal to angle 4. So, we can rewrite the equation as:
280 + angle 2 + angle 2 = 360
2 * angle 2 = 360 - 280
2 * angle 2 = 80
Dividing both sides by 2:
angle 2 = 40
So, we have found that angle 2 is equal to 40 degrees, which means that option b, angle 2 = 40 degrees and angle 3 = 70 degrees, is the correct answer.