Notice that a triangle with angles ∠ 1, ∠ 8, and ∠ 11 is isosceles.
30
Practice makes perfect
Let's analyze the given quadrilateral so that we can find the measure of ∠ 8.
Because our quadrilateral is a rectangle, its diagonals are congruent. Additionally, our quadrilateral is also a parallelogram, so its diagonals bisect each other. Therefore, the triangle with angles ∠ 1, ∠ 8, and ∠ 11 is an isosceles triangle.
Since ∠ 8 and ∠ 1 are the angles opposite the congruent sides, they are congruent. We are also given that m∠ 1= 30.
m ∠ 8=m ∠ 1 ⇔ m ∠ 8 = 30
