If parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Therefore, ∠ 1 and ∠ 5 are congruent. The measure of ∠ 1 is given as 30.
m ∠ 5=m ∠ 1 ⇔ m ∠ 5 = 30
Since 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 ∠ 4, ∠ 5, and ∠ 12 is isosceles.
Since ∠ 4 and ∠ 5 are the angles opposite the congruent sides, they are congruent.
m ∠ 4=m ∠ 5 ⇔ m ∠ 4 = 30
Finally, we will use the Triangle Angle-Sum Theorem.
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
We can use this theorem and the fact that m∠ 4=m∠ 5= 30 to find the measure of ∠ 12.
m∠ 4+m∠ 5+m∠ 12=180
⇕
30+ 30+m∠ 12=180
Let's solve the above equation!
