Question

ᴘʟᴢ ᴅᴏɴ'ᴛ sᴘᴀᴍ
Rɪɢʜᴛ ᴀɴsᴡᴇʀs ᴡɪʟʟ ʙᴇ ᴍᴀʀᴋᴇᴅ ᴀs ʙʀᴀɪɴʟɪᴇsᴛ ✅✅
Wʀᴏɴɢ ᴏʀ sᴘᴀᴍ ᴀɴs ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ ❎❎
ɪᴛ's ᴠᴇʀʏ ᴜʀɢᴇɴᴛ​

Answer 1

★ Given:-

• AC is a straight line

• ∠AOB = 50°

• ∠COD = 25°

• OE ⊥ AC So,

1. ∠AOE = 90°
2. ∠COE = 90°

★ To Find:-

• Value of ∠BOC

• Complement of ∠COD

• Value of complement of ∠COD

• Name of pair of supllementary angles

• Name of type of ∠BOE

★ Property Used:-

• Sum of Angles on straight line is 180°

• Sum of pair of complementary angle is 90°

• Sum of pair of supplementary angle is 180°

★ Solution:-

➲ Finding the value of ∠BOC

According to given conditions;

AC is a straight line

Sum of angles on straight line = 180°

➟ ∠AOB + ∠BOC = 180°

Putting the given value of ∠AOB

➟ 50° + ∠BOC = 180°

Now, Solving the equation

➟ 50° + ∠BOC = 180°

➟ ∠BOC = 180° - 50°

➟ ∠BOC = 130°

∴ Value of ∠BOC = 130°

➲ Finding Complement of ∠COD

As we know,

Sum of Complementary angles = 90°

According to given conditions;

➟ ∠COE = 90°

➟ ∠COD + ∠DOE = 90°

∴ Complement of ∠COD is ∠DOE

➲ Finding Value of Complement of ∠COD

According to given conditions;

Sum of complementary angles = 180°

➟ ∠COD + ∠DOE = 90°

➟ ∠25° + ∠DOE = 90°

➟ ∠DOE = 90° - 25°

➟ ∠DOE = 65°

∴ Value of complement of ∠COD is 65°

➲ Finding a pair of supplementary angles

As we know,

Sum of supplementary angles is 180°

As,

AC is a line than its sum of angles is 180°

∠AOB + ∠BOC = 180°

As its sum is 180°

∴ Pair of supplementary angles are ∠AOB and ∠BOC

➲ Finding type of ∠BOE

According to given conditions;

∠BOE = ∠AOB + ∠AOE

= 50 + 90

= 140°

As, ∠BOE is greater than 90° and less than 180°

∴ ∠BOE = Obtuse angles

Answer:-

1. Value of ∠BOC = 130°
2. Complement of ∠COD is ∠DOE ; Value of complement of ∠COD is 65°
3. Pair of supplementary angles are ∠AOB and ∠BOC
4. ∠BOE = Obtuse angles