Question

In Fig. 5.25, PQR = angle PRQ, then prove that anglePQS = angle PRT

no spam

otherwise report mide it ​

Answer 1

Answer:

sᴛ ɪs ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴀɴᴅ sᴜᴍ ᴏғ ᴀɴɢʟᴇ ɪɴ ʟɪɴᴇᴀʀ ᴘᴀɪʀ ᴀʟᴡᴀʏs ᴇǫᴜᴀʟ ᴛᴏ 180

∠ᴘǫs + ∠ᴘǫʀ = 180° … (1)

ᴀɴᴅ

∠ᴘʀᴛ + ∠ᴘʀǫ = 180° … (2)

ғʀᴏᴍ ᴇǫᴜᴀᴛɪᴏɴ (1) ᴀɴᴅ (2) .ᴡᴇ ɢᴇᴛ:

∠ᴘǫs + ∠ᴘǫʀ = ∠ᴘʀᴛ + ∠ᴘʀǫ … (3)

ʙᴜᴛ ɢɪᴠᴇɴ ᴛʜᴀᴛ ∠ᴘǫʀ = ∠ᴘʀǫ

ᴘʟᴜɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴡᴇ ɢᴇᴛ

∠ᴘǫs + ∠ᴘʀǫ =∠ᴘʀᴛ + ∠ᴘʀǫ

∠ᴘǫs = ∠ᴘʀᴛ + ∠ᴘʀǫ - ∠ᴘʀǫ

∠ᴘǫs = ∠ᴘʀᴛ

ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ