Question

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.


Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p

In which step did the student first make a mistake and how can it be corrected?
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A) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
B) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
C) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
D) Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Answer 1

Answer:

ᴛʜᴇ ғɪʀsᴛ ɪs ɪғ ᴛʜᴇ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢʟᴇs, ᴛʜᴇ ᴀɴɢʟᴇs ᴛʜᴀᴛ ᴀʀᴇ ᴏɴ ᴛʜᴇ sᴀᴍᴇ ᴄᴏʀɴᴇʀ ᴀᴛ ᴇᴀᴄʜ ɪɴᴛᴇʀsᴇᴄᴛɪᴏɴ, ᴀʀᴇ ᴇǫᴜᴀʟ, ᴛʜᴇɴ ᴛʜᴇ ʟɪɴᴇs ᴀʀᴇ ᴘᴀʀᴀʟʟᴇʟ. ᴛʜᴇ sᴇᴄᴏɴᴅ ɪs ɪғ ᴛʜᴇ ᴀʟᴛᴇʀɴᴀᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇs, ᴛʜᴇ ᴀɴɢʟᴇs ᴛʜᴀᴛ ᴀʀᴇ ᴏɴ ᴏᴘᴘᴏsɪᴛᴇ sɪᴅᴇs ᴏғ ᴛʜᴇ ᴛʀᴀɴsᴠᴇʀsᴀʟ ᴀɴᴅ ɪɴsɪᴅᴇ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟ ʟɪɴᴇs, ᴀʀᴇ ᴇǫᴜᴀʟ, ᴛʜᴇɴ ᴛʜᴇ ʟɪɴᴇs ᴀʀᴇ ᴘᴀʀᴀʟʟᴇʟ.

Answer 2

Answer:

D) is the correct answer.