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.
To find the measures of angles 2 and 3, we need to use the properties of a rhombus.
In a rhombus, opposite angles are congruent. This means that m<1 = m<3.
Since m<1 is given as 140°, we know that m<3 is also 140°.
Now, to find m<2, we can use the fact that the sum of the angles in a quadrilateral is 360°.
In a rhombus, the sum of the measures of all four angles is 360°.
So, m<1 + m<2 + m<3 + m<4 = 360°.
Substituting the known values, we have 140° + m<2 + 140° + m<4 = 360°.
Simplifying the equation, we have:
280° + m<2 + m<4 = 360°.
To find m<2 and m<4, we need to solve for them. We can simplify the equation further by subtracting 280° from both sides:
m<2 + m<4 = 80°.
Since opposite angles in a rhombus are congruent, m<2 = m<4. We can rewrite the equation as:
2(m<2) = 80°.
Dividing both sides by 2, we get:
m<2 = 40°.
Therefore, m<2 = 40° and m<3 = 140°.