Question

One of the acute angles of a right triangle 36°,find the other.​

Answer 1

♡ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴏɴᴇ ᴏғ ᴛʜᴇ ᴀᴄᴜᴛᴇ ᴀɴɢʟᴇ ᴏғ ᴀ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ɪs 36° , ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴀɴ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ ᴀʟᴡᴀʏs ʜᴀᴠᴇ ᴀɴ 90° ᴀɴɢʟᴇ♡

✦ Let the three angles be ∠A, ∠B, ∠C

• ❐∠A = 36°
• ❐∠B = 90°
• ❐∠C = x

( ✹ ᴀs ᴛʜᴇ ᴀɴɢʟᴇ C ɪs ᴜɴᴋɴᴏᴡɴ sᴏ ᴡᴇ ʜᴀᴠᴇ ᴘᴜᴛ x✹ )

Nᴏᴡ❥ ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴇ sᴜᴍ ᴏғ ᴛʜᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs 180° ✿

$\large\rm \red { \: \: \: \: \: \: \: \: \: 36° + 90° + ∠C = 180 ° } \\ \\ \large \rm \implies \red{126° + ∠C = 180° } \\ \\ \large \rm \implies \red{ ∠C = 180° - 126° } \\ \\ \large \rm \implies \red{ ∠C = 54° }$

• ☀︎ ʜᴇʀᴇ ᴡᴇ ɢᴏᴛ ᴛʜᴇ ᴏᴛʜᴇʀ ᴀɴɢʟᴇ, 54° ᴡʜɪᴄʜ ᴡᴇ ɴᴇᴇᴅᴇᴅ ᴛᴏ ғɪɴᴅ✔️☀︎

Answer 2

Answer :-

Given,

Triangle is Right angled

Acute angle = 36°

To find,

Third angle

Solution,

As the triangle is right angled,

$\purple{\boxed{\sf{Angle\: 1=36°\: and\: other\: angle=90°}}}$

$\orange{\boxed{\sf{Sum\: of\: all\: angles\: of\: triangle\: is\: 180°}}}$

Now,

90°+36°+x=180°

126°+x=180°

x=180°-126°

x=54°

$\large\pink{\boxed{\sf{Third\: angle\: is\: 54°}}}$

Hope it helps..

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