Question

step 1: m∠8 = 60, because m∠1 + m∠7 + m∠8 = 180. step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles. step 3: so, m∠12 = 60°. use the drop - down menus to explain whether or not stuart is correct. click the arrows to choose an answer from each menu. the sum of ∠1, ∠7, and ∠8 is choose..., ∠8 and ∠12 are choose... angles. the measure of ∠12 must be choose..., stuart is choose...

Explanation:

Step1: Recall angle - sum property

The sum of angles in a triangle is 180°. In the given figure, if we assume the triangle formed by the intersection of the lines, the sum of ∠1, ∠7, and ∠8 is 180°.

Step2: Identify corresponding - angle property

Corresponding angles are congruent when two parallel lines are cut by a transversal. ∠8 and ∠12 are corresponding angles.

Step3: Determine the measure of ∠12

Since ∠8 and ∠12 are corresponding angles and if m∠8 = 60° (as given in the steps in the problem - statement), then m∠12=60°.

Answer:

The sum of ∠1, ∠7, and ∠8 is 180°. ∠8 and ∠12 are corresponding angles. The measure of ∠12 must be 60°. Stuart is correct.