In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.

So all you have to know that sets stuart wrong is that angle 12 is not 69 degrees. So the dropdowns as follows. Angle 1, 7 and 8 make one triangle and have equal degrees. So 180 equals a whole triangle. Angle 12 and 8 are on the same side and inside the triangle. (Remember 1,7,8? well divide 180 by 3 and u get angle 8 being 60. Same as angle 7. The interior trapezoid will be 60+60+120+120=360.) Angle 12= 120 thus Stuart is wrong.

oeerivona oeerivona · Answer 2 · 2021-12-10T14:21:07+01:00

The reasoning that may be used for finding the measure of m∠12, is the

same side interior angles theorem.

The correct options using the drop-down menu are;

The sum of ∠1, ∠7, and ∠8 is 180°

∠8 and ∠12 are same side interior angles

The measure of ∠12 must be = 120°

Stuart is not correct

Reasons:

Given parameters;

Line x ║ line y

m∠1 = 65°, m∠7 = 55°

m∠12 = 60°

Stuart states ∠12 = 60°

The reasoning is presented as follows;

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°

Using the drop-down menu, we have;

The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)

∠8 and ∠12 are same side interior angles (by definition)

Same side interior angles are supplementary, therefore;

∠8 +∠12 = 180°

∠12 = 180° - ∠8

Which gives;

The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°

The measure of ∠12 must be = 120°

Stuart is not correct

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