Notice that a triangle with angles ∠ 2, ∠ 3, and ∠ 10 is isosceles.
60
Practice makes perfect
Let's analyze the given quadrilateral so that we can find the measure of ∠ 3.
By the definition of a rectangle, we know that WXYZ has four right angles. Therefore, the measure of m ∠ WXZ is 90.
m ∠ WXZ= 90
With the Angle Addition Postulate we can express m ∠ WXZ as a sum of m ∠ 1 and m ∠ 2.
m ∠ 1 + m ∠ 2 = m ∠ WXZ
⇕
m ∠ 1 + m ∠ 2 = 90
We are given that m ∠ 1= 30. Let's substitute this value into our equation and solve for m∠ 2.
Because our quadrilateral is a rectangle, its diagonals are congruent. Since our quadrilateral is also a parallelogram, its diagonals bisect each other. Therefore, the triangle with angles ∠ 2, ∠ 3, and ∠ 10 is an isosceles triangle.
Since ∠ 3 and ∠ 2 are the angles opposite the congruent sides, they are congruent. Remember we have found that the measure of ∠ 2 is 60.
m ∠ 3=m ∠ 2 ⇔ m ∠ 3 = 60
