Question

2. If 1 || m, 21 = 60°, Z2 = 120°, 24 = 120°, find measure of each of the remaining angles. 2 3 4 6. 5 co 7 8.​

Answer 1

Answer:

l II m and p is their transversal and 1 = 120°

∠1 + ∠2 = 180 °(Straight line)

120° + ∠2 = 180° > ∠2 = 180° - 120° = 60°

∠2 = 60°

But ∠1 = ∠3 (Vertically opposite angles)

∠3 = ∠1 = 120°

Similarly ∠4 = ∠2

(Vertically opposite angles)

∠4 = 60°

∠5 = ∠1 (Corresponding angles)

∠5 = 120°

Similarly ∠6 = ∠2 (Corresponding angles)

∠6 = 60°

∠7 = ∠5 (Vertically opposite angles)

∠7 = 120°

And ∠8 = ∠6 (Vertically opposite angles)

∠8 = 60°

Hence ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°

Step-by-step explanation:

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Answer 2

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ʟ ɪɪ ᴍ ᴀɴᴅ ᴘ ɪs ᴛʜᴇɪʀ ᴛʀᴀɴsᴠᴇʀsᴀʟ ᴀɴᴅ 1 = 120°

∠1 + ∠2 = 180 °(sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ)

120° + ∠2 = 180° > ∠2 = 180° - 120° = 60°

∠2 = 60°

ʙᴜᴛ ∠1 = ∠3 (ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇs)

∠3 = ∠1 = 120°

sɪᴍɪʟᴀʀʟʏ ∠4 = ∠2

(ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇs)

∠4 = 60°

∠5 = ∠1 (ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢʟᴇs)

∠5 = 120°

sɪᴍɪʟᴀʀʟʏ ∠6 = ∠2 (ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢʟᴇs)

∠6 = 60°

∠7 = ∠5 (ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇs)

∠7 = 120°

ᴀɴᴅ ∠8 = ∠6 (ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇs)

∠8 = 60°

ʜᴇɴᴄᴇ ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° ᴀɴᴅ ∠8 = 60°.

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