Question

In the diagram, line x is parallel to line y, m <1 = and and L7 = 55°
Stuart says that
m<12 = 60°
His reasoning is shown.
Step 1: mL8 = 60°, because m<1 + mL7 + mL8 = 180'
Step 2: 28 = L12, because 28 and 212 are corresponding angles.
Step 3: So, mL12 = 60°
Use the drop-down menus to explain whether or not Stuart is correct.
10/11
5
12\13
→X
8
Click the arrows to choose an answer from each menu.
The sum of L1, 47, and 28 is Choose... angles. The measure of Z12 must be Choose...
. L8 and 12 are
• Stuart is
Choose...
Choose...

Answer 1

To evaluate Stuart's reasoning and determine if he is correct, let's analyze each step with the relevant information.

1. **Step 1: m<8 = 60°, because m<1 + m<7 + m<8 = 180°**
- Since line x is parallel to line y, we can use the fact that angles on a straight line sum up to 180°. Stuart claims that m<8 is 60° by using the sum of angles at a point. However, we first need to find m<1 + m<7. Given that m<1 = 55° and m<7 = 55°, then m<1 + m<7 = 55° + 55° = 110°.
- This means m<8 should actually be:
\( m<8 = 180° - 110° = 70°\).
- Therefore, Stuart's claim that m<8 is 60° is incorrect.

2. **Step 2: m<8 = m<12, because m<8 and m<12 are corresponding angles.**
- If lines x and y are parallel, then indeed, corresponding angles are equal. So, if m<8 is 70° (as calculated), then m<12 = 70°.

3. **Step 3: So, m<12 = 60°**
- This conclusion is based on the previous step, and since we established that m<8 = 70°, then m<12 cannot be 60°. Instead, m<12 = 70°.

Based on the analysis of each step:

- **The sum of m<1, m<7, and m<8 is**: **110°** (not 180° as needed for m<8 to be 60°).
- **The measure of m<12 must be**: **70°**, not 60°.
- **m<8 and m<12 are corresponding angles**.

Thus, Stuart is:

- **Stuart is incorrect.**

Please complete the drop-down menus with the following choices based on the analysis:

1. The sum of m<1, m<7, and m<8 is: **110° (not 180°)».
2. The measure of m<12 must be: **70° (not 60°)».
3. m<8 and m<12 are: **corresponding angles, but with incorrect measurements due to Stuart's error.**
4. **Stuart is incorrect.**